{ "protocol": { "exam.json": "f189ea0fc59630a271a4455128917b65329661aff00d3b8efa82361dbcd91608", "exam.md": "7e3770f853599fe647fa1c9882cc8b864151b2b249e2b2a83115eea7f5240031", "requests.json": "db1d5220d099c4e7dc43b462b3be5ab2c6a1045e4a2909b4a865d74fc57a5024" }, "exam": { "version": "1.0", "instructions": "Select the best answer for single-choice items and all correct options for select-all items. Mathematical expressions are exact; exp(x)=e^x. No calculator, external tools, retrieval, worked solutions or answer feedback. Answer each item from its stated context. All questions are independent API judgments; no previous correct answers are supplied.", "items": [ { "id": "Q1.1", "section": 1, "context": "", "prompt": "Is ((P AND Q) IMPLIES R) equivalent to (P IMPLIES (Q IMPLIES R))?", "response_mode": "single_choice", "options": { "A": "Always True", "B": "Sometimes False" } }, { "id": "Q1.2", "section": 1, "context": "", "prompt": "Is [forall x, (P(x) IMPLIES Q(x))] equivalent to [(forall x, NOT P(x)) OR (forall x, Q(x))]?", "response_mode": "single_choice", "options": { "A": "Always True", "B": "Sometimes False" } }, { "id": "Q2.1", "section": 2, "context": "", "prompt": "For integers a,b, let d=gcd(a,b). Which argument proves that d divides ax+by for every pair of integers x,y?", "response_mode": "single_choice", "options": { "A": "Since d divides a and b, Bezout gives ax+by=d for every pair of integers x,y. Therefore ax+by is always equal to d and hence divisible by d.", "B": "Since d divides a and b, write d=ak and d=bj for integers k,j. Substituting gives ax+by=d(x/k+y/j), whose parenthesized term must be an integer.", "C": "Since d divides a and b, write a=dk and b=dj for integers k,j. Then ax+by=d(kx+jy), and kx+jy is an integer, establishing divisibility.", "D": "Since d is the greatest common divisor, every integer smaller than d divides both a and b. In particular x and y divide both, so d divides ax+by." } }, { "id": "Q2.2", "section": 2, "context": "", "prompt": "7 divides 4^186 - 1. Hint: 186 = 31 * 6.", "response_mode": "single_choice", "options": { "A": "True", "B": "False" } }, { "id": "Q2.3", "section": 2, "context": "", "prompt": "5 divides 4^n - 1 for all even natural numbers n.", "response_mode": "single_choice", "options": { "A": "True", "B": "False" } }, { "id": "Q2.4", "section": 2, "context": "", "prompt": "What is the last digit (ones place) of 3^47?", "response_mode": "single_choice", "options": { "A": "2", "B": "9", "C": "1", "D": "3", "E": "5", "F": "6", "G": "4", "H": "8", "I": "0", "J": "7" } }, { "id": "Q2.5", "section": 2, "context": "", "prompt": "Alice implements RSA correctly with N=33 and e=7 and sends ciphertext y=6. Given 33=3*11, what was the original message x?", "response_mode": "single_choice", "options": { "A": "15", "B": "27", "C": "18", "D": "6" } }, { "id": "Q2.6", "section": 2, "context": "", "prompt": "Find (6^7 + 7^6) mod 91. Hint: use CRT; 91=7*13.", "response_mode": "single_choice", "options": { "A": "13", "B": "6", "C": "0", "D": "78" } }, { "id": "Q3.1", "section": 3, "context": "", "prompt": "Working modulo 6, how many distinct formal polynomials of degree exactly two are there?", "response_mode": "single_choice", "options": { "A": "125", "B": "180", "C": "216", "D": "150" } }, { "id": "Q3.2", "section": 3, "context": "", "prompt": "Over GF(7), find g(x) of degree strictly less than 7, with coefficients in GF(7), giving the same output as f(x)=9x^66+7x^58+5x^55+5x^24+10x^19 for every x in GF(7). Hint: the solution is a simple polynomial.", "response_mode": "single_choice", "options": { "A": "g(x)=x^6", "B": "g(x)=0", "C": "g(x)=1", "D": "g(x)=x" } }, { "id": "Q3.3", "section": 3, "context": "", "prompt": "You receive n+2k points from a polynomial of degree n-1, with up to k corruptions. How many messages can you recover using Berlekamp-Welch?", "response_mode": "single_choice", "options": { "A": "k", "B": "n+2k", "C": "n", "D": "1" } }, { "id": "Q4.1", "section": 4, "context": "", "prompt": "K_4 is planar.", "response_mode": "single_choice", "options": { "A": "True", "B": "False" } }, { "id": "Q4.2", "section": 4, "context": "", "prompt": "K_5 has an Eulerian tour.", "response_mode": "single_choice", "options": { "A": "True", "B": "False" } }, { "id": "Q4.3", "section": 4, "context": "", "prompt": "A 12-sided die is a planar graph wrapped around a sphere, with 12 faces and 20 vertices. How many edges does it have?", "response_mode": "single_choice", "options": { "A": "18", "B": "24", "C": "32", "D": "30" } }, { "id": "Q4.4", "section": 4, "context": "", "prompt": "Which argument proves that, if a finite undirected graph has one odd-degree vertex, it must have another odd-degree vertex?", "response_mode": "single_choice", "options": { "A": "The sum of degrees equals twice the number of edges, so it is even. If exactly one degree were odd and all others even, that sum would be odd, a contradiction.", "B": "Removing any odd-degree vertex leaves all remaining degrees even. Restoring it changes every remaining degree by one, so every other vertex then has odd degree.", "C": "An edge incident to the odd-degree vertex has another endpoint. That endpoint has odd degree because the common edge contributes one to both endpoint degrees.", "D": "The sum of degrees equals the number of edges, so it is even. If exactly one degree were odd and all others even, that sum would be odd, a contradiction." } }, { "id": "Q5.1", "section": 5, "context": "State whether each set is Finite, Countably Infinite, or Uncountably Infinite.", "prompt": "The set of all complex numbers.", "response_mode": "single_choice", "options": { "A": "Finite", "B": "Countably Infinite", "C": "Uncountably Infinite" } }, { "id": "Q5.2", "section": 5, "context": "State whether each set is Finite, Countably Infinite, or Uncountably Infinite.", "prompt": "The set of all prime numbers.", "response_mode": "single_choice", "options": { "A": "Finite", "B": "Countably Infinite", "C": "Uncountably Infinite" } }, { "id": "Q5.3", "section": 5, "context": "State whether each set is Finite, Countably Infinite, or Uncountably Infinite.", "prompt": "The real interval [0.001,0.1].", "response_mode": "single_choice", "options": { "A": "Finite", "B": "Countably Infinite", "C": "Uncountably Infinite" } }, { "id": "Q5.4", "section": 5, "context": "State whether each set is Finite, Countably Infinite, or Uncountably Infinite.", "prompt": "The complex numbers a+bi where a,b are integers.", "response_mode": "single_choice", "options": { "A": "Finite", "B": "Countably Infinite", "C": "Uncountably Infinite" } }, { "id": "Q5.5", "section": 5, "context": "State whether each set is Finite, Countably Infinite, or Uncountably Infinite.", "prompt": "The set of edges of the complete bipartite graph K_(100,100).", "response_mode": "single_choice", "options": { "A": "Finite", "B": "Countably Infinite", "C": "Uncountably Infinite" } }, { "id": "Q5.6", "section": 5, "context": "State whether each set is Finite, Countably Infinite, or Uncountably Infinite.", "prompt": "The set of all integer powers of 2.", "response_mode": "single_choice", "options": { "A": "Finite", "B": "Countably Infinite", "C": "Uncountably Infinite" } }, { "id": "Q5.7", "section": 5, "context": "State whether each set is Finite, Countably Infinite, or Uncountably Infinite.", "prompt": "The set of real polynomials of degree at most two passing through (1,1) and (2,2).", "response_mode": "single_choice", "options": { "A": "Finite", "B": "Countably Infinite", "C": "Uncountably Infinite" } }, { "id": "Q6", "section": 6, "context": "Two programs F and G are equivalent if, for every input, both halt with the same output or both do not halt. Suppose EQUIVALENT(F,G) always halts and returns TRUE iff F and G are equivalent. Complete HALT(P,x) to decide whether P halts on x:\ndef HALT(P,x):\n def F(y):\n ----(1)----\n ----(2)----\n def G(y):\n return 0\n return EQUIVALENT(----(3)----, ----(4)----)", "prompt": "Choose the ordered tuple filling blanks (1),(2),(3),(4).", "response_mode": "single_choice", "options": { "A": "(return 0; P(x); F; G)", "B": "(P(x); return 0; F; G)", "C": "(P(x); return 0; F; F)", "D": "(P(y); return 0; F; G)" } }, { "id": "Q7.1", "section": 7, "context": "Answers may be unsimplified (binomial coefficients, factorials, exponents), but do not use summation or product notation. C(n,k) denotes a binomial coefficient.", "prompt": "A deck has 52 cards, 4 suits and 13 ranks per suit. A hand is an unordered set of five cards. How many hands contain exactly one 6 and exactly one 7?", "response_mode": "single_choice", "options": { "A": "C(4,2)*C(44,3)", "B": "4*4*C(50,3)", "C": "4*4*C(44,3)", "D": "4*4*C(44,3)*5!" } }, { "id": "Q7.2", "section": 7, "context": "Answers may be unsimplified (binomial coefficients, factorials, exponents), but do not use summation or product notation. C(n,k) denotes a binomial coefficient.", "prompt": "Draw 3 cards without replacement. A means at least one ace. C_i means exactly i aces, for i=1,2,3. F,S,T mean respectively that the first, second or third card is an ace. Which representation of P(A) is easier, and why?", "response_mode": "single_choice", "options": { "A": "Use C_1,C_2,C_3: they are independent and their intersection is A, so their probabilities can be multiplied.", "B": "Use F,S,T: they are independent and their intersection is A, so their probabilities can be multiplied.", "C": "Use F,S,T: they are mutually exclusive and their union is A, so their probabilities can be added.", "D": "Use C_1,C_2,C_3: they are mutually exclusive and their union is A, so their probabilities can be added." } }, { "id": "Q7.3", "section": 7, "context": "Answers may be unsimplified (binomial coefficients, factorials, exponents), but do not use summation or product notation. C(n,k) denotes a binomial coefficient.\n\nAgnes distributes all 40 indistinguishable cookies among three distinct minions: Bob, Kevin and Stuart. Each has a carrying limit of 15 cookies.", "prompt": "With no carrying limit, how many distributions of the 40 cookies are possible?", "response_mode": "single_choice", "options": { "A": "C(40,2)", "B": "3^40", "C": "C(42,2)", "D": "C(42,3)" } }, { "id": "Q7.4", "section": 7, "context": "Answers may be unsimplified (binomial coefficients, factorials, exponents), but do not use summation or product notation. C(n,k) denotes a binomial coefficient.\n\nAgnes distributes all 40 indistinguishable cookies among three distinct minions: Bob, Kevin and Stuart. Each has a carrying limit of 15 cookies.", "prompt": "How many distributions exceed Bob's limit? Other minions may also exceed their limits.", "response_mode": "single_choice", "options": { "A": "C(26,2)", "B": "C(27,2)", "C": "C(42,2)-C(26,2)", "D": "C(24,2)" } }, { "id": "Q7.5", "section": 7, "context": "Answers may be unsimplified (binomial coefficients, factorials, exponents), but do not use summation or product notation. C(n,k) denotes a binomial coefficient.\n\nAgnes distributes all 40 indistinguishable cookies among three distinct minions: Bob, Kevin and Stuart. Each has a carrying limit of 15 cookies.", "prompt": "How many distributions exceed both Bob's and Kevin's limits?", "response_mode": "single_choice", "options": { "A": "C(12,2)", "B": "C(10,2)", "C": "C(8,2)", "D": "C(26,2)^2" } }, { "id": "Q7.6", "section": 7, "context": "Answers may be unsimplified (binomial coefficients, factorials, exponents), but do not use summation or product notation. C(n,k) denotes a binomial coefficient.\n\nAgnes distributes all 40 indistinguishable cookies among three distinct minions: Bob, Kevin and Stuart. Each has a carrying limit of 15 cookies. Here a counts unrestricted distributions; b counts distributions exceeding one specified limit; c counts distributions exceeding two specified limits.", "prompt": "Let a,b,c denote the answers to Q7.3,Q7.4,Q7.5 respectively. Express the number of distributions respecting all three limits in terms of a,b,c.", "response_mode": "single_choice", "options": { "A": "a-b+c", "B": "a-3*b+6*c", "C": "a-3*b+3*c", "D": "a-3*b-3*c" } }, { "id": "Q8", "section": 8, "context": "", "prompt": "In a town, 3/4 of residents have black hair and 2/3 are female, independently. Two people are selected randomly with replacement. Given that at least one is a black-haired female, what is the probability both have black hair? Select the answer with valid supporting work. Hint: the answer is not 9/16.", "response_mode": "single_choice", "options": { "A": "1/2: a randomly selected person is a black-haired female with probability (3/4)*(2/3)=1/2; replacement makes the requested conditional probability the same.", "B": "8/9: conditional on both people having black hair, the chance at least one is female is 1-(1/3)^2=8/9; this is the requested conditional probability.", "C": "3/4: if A means at least one black-haired female and B means both have black hair, then P(B|A)=P(B)/P(A)=(9/16)/(1-(1/2)^2)=3/4.", "D": "2/3: if A means at least one black-haired female and B means both have black hair, then P(B|A)=(9/16)*(1-(1/3)^2)/(1-(1/2)^2)=2/3." } }, { "id": "Q9.2", "section": 9, "context": "Flip a biased coin independently infinitely many times, with heads probability p and tails probability 1-p. Give the distribution and parameters. The common discrete distributions named on the exam are Bernoulli, Binomial, Geometric, Uniform and Poisson. Original worked example Q9.1 (0 points): the indicator that the first three flips are heads is Bernoulli(p^3). Geometric(q) counts trials up to and including the first success (support 1,2,...).", "prompt": "Distribution of the number of heads in the first 70 flips?", "response_mode": "single_choice", "options": { "A": "Poisson(70*p)", "B": "Geometric(p)", "C": "Binomial(70,1-p)", "D": "Binomial(70,p)" } }, { "id": "Q9.3", "section": 9, "context": "Flip a biased coin independently infinitely many times, with heads probability p and tails probability 1-p. Give the distribution and parameters. The common discrete distributions named on the exam are Bernoulli, Binomial, Geometric, Uniform and Poisson. Original worked example Q9.1 (0 points): the indicator that the first three flips are heads is Bernoulli(p^3). Geometric(q) counts trials up to and including the first success (support 1,2,...).", "prompt": "Conditional on exactly one head in the first 20 flips, what is the distribution of the flip number on which the first head occurs?", "response_mode": "single_choice", "options": { "A": "Geometric(p)", "B": "Uniform({1,2,...,20})", "C": "Binomial(20,p)", "D": "Uniform({0,1,...,19})" } }, { "id": "Q9.4", "section": 9, "context": "Flip a biased coin independently infinitely many times, with heads probability p and tails probability 1-p. Give the distribution and parameters. The common discrete distributions named on the exam are Bernoulli, Binomial, Geometric, Uniform and Poisson. Original worked example Q9.1 (0 points): the indicator that the first three flips are heads is Bernoulli(p^3). Geometric(q) counts trials up to and including the first success (support 1,2,...).", "prompt": "Distribution of the gap between the first two tails, counting intervening heads? THHHT has gap 3. Hint: a standard random variable minus 1.", "response_mode": "single_choice", "options": { "A": "Geometric(p)-1", "B": "Geometric(1-p)-1", "C": "Binomial(2,p)-1", "D": "Geometric(1-p)" } }, { "id": "Q9.5", "section": 9, "context": "Flip a biased coin independently infinitely many times, with heads probability p and tails probability 1-p. Give the distribution and parameters. The common discrete distributions named on the exam are Bernoulli, Binomial, Geometric, Uniform and Poisson. Original worked example Q9.1 (0 points): the indicator that the first three flips are heads is Bernoulli(p^3). Geometric(q) counts trials up to and including the first success (support 1,2,...).", "prompt": "Let p=1/2. Distribution of the number of flips until the same outcome occurs twice consecutively? Hint: 1 plus a standard random variable.", "response_mode": "single_choice", "options": { "A": "1+Geometric(1/2)", "B": "1+Binomial(2,1/2)", "C": "Geometric(1/2)", "D": "1+Geometric(1/4)" } }, { "id": "Q9.6", "section": 9, "context": "Flip a biased coin independently infinitely many times, with heads probability p and tails probability 1-p. Give the distribution and parameters. The common discrete distributions named on the exam are Bernoulli, Binomial, Geometric, Uniform and Poisson. Original worked example Q9.1 (0 points): the indicator that the first three flips are heads is Bernoulli(p^3). Geometric(q) counts trials up to and including the first success (support 1,2,...).", "prompt": "Let p=1/2. Distribution of the number of runs in the first 50 flips? A run is an uninterrupted sequence of identical outcomes, e.g. HHHHHTTTHTTH begins with runs HHHHH, TTT, H, TT. Hint: 1 plus a standard random variable.", "response_mode": "single_choice", "options": { "A": "1+Geometric(1/2)", "B": "1+Binomial(50,1/2)", "C": "1+Binomial(49,1/4)", "D": "1+Binomial(49,1/2)" } }, { "id": "Q10", "section": 10, "context": "Each spin has four equally likely outcomes: alpha earns 1 point; beta earns 2 points; gamma gives two additional spins; delta loses 1 point and gives one additional spin. Start with one spin. Additional spins use the same rules. The score is the sum of points earned or lost. Example: alpha gives score 1. Example sequence delta,gamma,gamma,alpha,beta,alpha gives score -1+1+2+1=3.", "prompt": "Let X be the final score. What is E[X]?", "response_mode": "single_choice", "options": { "A": "0", "B": "1", "C": "2", "D": "3", "E": "4", "F": "infinity" } }, { "id": "Q11.1", "section": 11, "context": "Normal(mu,v) denotes a normal distribution with mean mu and variance v. Poisson parameters are positive.", "prompt": "Independent X~Normal(1,2) and Y~Normal(2,1). What is the distribution of Z=2X-Y+1?", "response_mode": "single_choice", "options": { "A": "Normal(1,5)", "B": "Normal(1,9)", "C": "Normal(1,3)", "D": "Normal(5,9)" } }, { "id": "Q11.2", "section": 11, "context": "Normal(mu,v) denotes a normal distribution with mean mu and variance v. Poisson parameters are positive.", "prompt": "Independent X,Y~Poisson(lambda). Let Z=X+Y. Select all true statements.", "response_mode": "select_all", "options": { "A": "Z~Poisson(2*lambda)", "B": "Z has the distribution of 2P, where P~Poisson(lambda)", "C": "None of the above" } }, { "id": "Q11.3", "section": 11, "context": "Normal(mu,v) denotes a normal distribution with mean mu and variance v. Poisson parameters are positive.", "prompt": "Let X_1,...,X_n be independent Poisson(lambda) variables and S=sum_i X_i. Select all true statements.", "response_mode": "select_all", "options": { "A": "For every n, S~Poisson(lambda*n)", "B": "As n tends to infinity, (S-lambda*n)/sqrt(lambda*n) converges in distribution to Normal(0,1)", "C": "None of the above" } }, { "id": "Q12.1", "section": 12, "context": "Student arrivals are modeled as a homogeneous Poisson process at a rate of one student per 30 minutes.", "prompt": "Nobody arrives during the first 50 minutes. What is the probability at least one student arrives during the final 10 minutes of the hour?", "response_mode": "single_choice", "options": { "A": "1-exp(-5/3)", "B": "1-exp(-1/3)", "C": "exp(-1/3)", "D": "1-exp(-2)" } }, { "id": "Q12.2", "section": 12, "context": "Student arrivals are modeled as a homogeneous Poisson process at a rate of one student per 30 minutes.", "prompt": "At the same arrival rate, students never leave once they arrive. Starting from an empty room, what is the expected number at the end of one hour?", "response_mode": "single_choice", "options": { "A": "30", "B": "2", "C": "1/2", "D": "1-exp(-2)" } }, { "id": "Q12.3", "section": 12, "context": "Time between BART train departures is exponential, with a mean of 15 minutes.", "prompt": "Ishan arrives at a random time. What is his expected wait until a train departs?", "response_mode": "single_choice", "options": { "A": "1/15 minute", "B": "15 minutes", "C": "7.5 minutes", "D": "30 minutes" } }, { "id": "Q12.4", "section": 12, "context": "Time between BART train departures is exponential, with a mean of 15 minutes.", "prompt": "The station agent says the last train left 5 minutes ago. What is Ishan's expected remaining wait?", "response_mode": "single_choice", "options": { "A": "15 minutes", "B": "20 minutes", "C": "10 minutes", "D": "5 minutes" } }, { "id": "Q12.5", "section": 12, "context": "", "prompt": "Trains and passengers have first arrival times A_t and A_p. The joint PDF is f(a_p,a_t)=lambda_p*lambda_t*exp(-lambda_p*a_p-lambda_t*a_t) for a_p,a_t>=0 and zero otherwise. Give an integral for P(A_t=1), clipped at 1?", "response_mode": "single_choice", "options": { "A": "1-(1-p^5)^12", "B": "min(1,12*p^5)", "C": "min(1,12*p^10)", "D": "min(1,p^5)" } }, { "id": "Q13.6", "section": 13, "context": "A 5 by 5 bingo card represents 25 booths. Melody visits each booth independently with probability p; its square is marked exactly when visited. There is no free square. The 12 possible bingo lines are 5 rows, 5 columns and 2 diagonals. X is the number of completely marked lines.", "prompt": "Assume E[X]<2. Which is the standard two-sided Chebyshev upper-bound expression applied to P(X>=2), in terms of E[X] and Var(X), clipped at 1?", "response_mode": "single_choice", "options": { "A": "min(1,(2-E[X])^2/Var(X))", "B": "min(1,Var(X)/(2-E[X]))", "C": "min(1,Var(X)/(2-E[X])^2)", "D": "min(1,Var(X)/(2+E[X])^2)" } }, { "id": "Q14", "section": 14, "context": "", "prompt": "Events A,B have nonzero probability and indicators I_A,I_B. Which argument proves that Cov(I_A,I_B)>0 implies P(A|B)>P(A)?", "response_mode": "single_choice", "options": { "A": "Cov(I_A,I_B)=P(A union B)-P(A)P(B)=P(B)[P(A|B)-P(A)]. Because P(B)>0, positive covariance forces the bracket to be positive.", "B": "Cov(I_A,I_B)=P(A intersection B)-P(A)P(B)=P(A)[P(A|B)-P(A)]. Because P(A)>0, positive covariance forces the bracket to be positive.", "C": "Cov(I_A,I_B)=P(A intersection B)-P(A)P(B)=P(B)[P(A|B)-P(A)]. Because P(B)>0, positive covariance forces the bracket to be positive.", "D": "Cov(I_A,I_B)=P(A)P(B)-P(A intersection B)=P(B)[P(A|B)-P(A)]. Because P(B)>0, positive covariance forces the bracket to be positive." } }, { "id": "Q15.1", "section": 15, "context": "Gaussian(mu,v) denotes a Gaussian distribution with mean mu and variance v.", "prompt": "Let X~Gaussian(3,6) and Y~Exponential(3) be independent. What is P(X=Y)?", "response_mode": "single_choice", "options": { "A": "0", "B": "Cannot be determined from the stated information", "C": "1", "D": "1/2" } }, { "id": "Q15.2", "section": 15, "context": "Gaussian(mu,v) denotes a Gaussian distribution with mean mu and variance v.", "prompt": "For X~Gaussian(3,6), which statement is true about P(X<4)?", "response_mode": "single_choice", "options": { "A": "<0.5", "B": "=0.5", "C": ">0.5", "D": "Not enough information" } }, { "id": "Q15.3", "section": 15, "context": "Gaussian(mu,v) denotes a Gaussian distribution with mean mu and variance v.\n\nA, B and C are independent Uniform(0,12) random variables. X indicates that C lies between A and B.", "prompt": "What is P(X=1 | A,B), in terms of A and B?", "response_mode": "single_choice", "options": { "A": "1-abs(A-B)/12", "B": "abs(A-B)/12", "C": "(A-B)/12", "D": "abs(A-B)/144" } }, { "id": "Q15.4", "section": 15, "context": "Gaussian(mu,v) denotes a Gaussian distribution with mean mu and variance v.\n\nA, B and C are independent Uniform(0,12) random variables. X indicates that C lies between A and B.", "prompt": "Without conditioning on A,B, what is P(X=1)? Hint: there is a way without integrals.", "response_mode": "single_choice", "options": { "A": "1/2", "B": "1/6", "C": "2/3", "D": "1/3" } }, { "id": "Q15.5", "section": 15, "context": "Gaussian(mu,v) denotes a Gaussian distribution with mean mu and variance v.\n\nA, B and C are independent Uniform(0,12) random variables. X indicates that C lies between A and B. Q15.3 asks for P(X=1 | A,B); Q15.4 asks for P(X=1).", "prompt": "What is E[abs(A-B)]? Hint: use the previous two parts to avoid integrals. The original exam labels this particularly challenging.", "response_mode": "single_choice", "options": { "A": "0", "B": "4", "C": "8", "D": "6" } }, { "id": "Q16.1", "section": 16, "context": "Tom travels from Chicago (CHI) to Miami (MIA). Each outgoing train route is equally likely. The diagram, transcribed without solving: CHI -> SFO (1/3), DC (1/3), NYC (1/3); SFO -> CHI (1); DC -> SFO (1/3), NYC (1/3), MIA (1/3); NYC -> CHI (1/2), DC (1/2); MIA -> MIA (1).", "prompt": "Find the probability of reaching MIA from CHI before visiting NYC. Select a system of equations, without solving it. h(s) denotes the probability of reaching MIA before NYC starting at s; the requested probability is h(CHI).", "response_mode": "single_choice", "options": { "A": "h(MIA)=1; h(NYC)=0; h(SFO)=h(CHI); h(DC)=(h(SFO)+h(NYC)+h(MIA))/3; h(CHI)=(h(SFO)+h(DC))/2.", "B": "h(MIA)=1; h(NYC)=0; h(SFO)=h(CHI); h(DC)=(h(NYC)+h(MIA))/2; h(CHI)=(h(SFO)+h(DC)+h(NYC))/3.", "C": "h(MIA)=0; h(NYC)=1; h(SFO)=h(CHI); h(DC)=(h(SFO)+h(NYC)+h(MIA))/3; h(CHI)=(h(SFO)+h(DC)+h(NYC))/3.", "D": "h(MIA)=1; h(NYC)=0; h(SFO)=h(CHI); h(DC)=(h(SFO)+h(NYC)+h(MIA))/3; h(CHI)=(h(SFO)+h(DC)+h(NYC))/3." } }, { "id": "Q16.2", "section": 16, "context": "Tom travels from Chicago (CHI) to Miami (MIA). Each outgoing train route is equally likely. The diagram, transcribed without solving: CHI -> SFO (1/3), DC (1/3), NYC (1/3); SFO -> CHI (1); DC -> SFO (1/3), NYC (1/3), MIA (1/3); NYC -> CHI (1/2), DC (1/2); MIA -> MIA (1).", "prompt": "Tom spends 3 days on each visit to NYC and 1 day in every other city before departing. Travel takes zero days. Select equations for the expected days to first arrival at MIA, starting in CHI and including its initial day. Do not solve. t(s) denotes the remaining expected days starting at s.", "response_mode": "single_choice", "options": { "A": "t(MIA)=0; t(SFO)=1+t(CHI); t(CHI)=1+(t(SFO)+t(DC)+t(NYC))/3; t(DC)=1+(t(NYC)+t(MIA))/3; t(NYC)=3+(t(CHI)+t(DC))/2.", "B": "t(MIA)=0; t(SFO)=1+t(CHI); t(CHI)=1+(t(SFO)+t(DC)+t(NYC))/3; t(DC)=1+(t(SFO)+t(NYC)+t(MIA))/3; t(NYC)=3+(t(CHI)+t(DC))/2.", "C": "t(MIA)=0; t(SFO)=1+t(CHI); t(CHI)=1+(t(SFO)+t(DC)+t(NYC))/3; t(DC)=1+(t(SFO)+t(NYC)+t(MIA))/3; t(NYC)=1+(t(CHI)+t(DC))/2.", "D": "t(MIA)=1; t(SFO)=1+t(CHI); t(CHI)=1+(t(SFO)+t(DC)+t(NYC))/3; t(DC)=1+(t(SFO)+t(NYC)+t(MIA))/3; t(NYC)=3+(t(CHI)+t(DC))/2." } } ] }, "run": { "scope": "full", "request_manifest_sha256": "db1d5220d099c4e7dc43b462b3be5ab2c6a1045e4a2909b4a865d74fc57a5024", "started_at": "2026-09-18T06:51:42.380907+00:00", "sections": [ { "section": 1, "request": { "model": "jev-1.13.0", "state": { "instructions": "Select the best answer for single-choice items and all correct options for select-all items. Mathematical expressions are exact; exp(x)=e^x. No calculator, external tools, retrieval, worked solutions or answer feedback. Answer each item from its stated context. All questions are independent API judgments; no previous correct answers are supplied.", "problems": [ { "id": "Q1.1", "context": "", "prompt": "Is ((P AND Q) IMPLIES R) equivalent to (P IMPLIES (Q IMPLIES R))?" }, { "id": "Q1.2", "context": "", "prompt": "Is [forall x, (P(x) IMPLIES Q(x))] equivalent to [(forall x, NOT P(x)) OR (forall x, Q(x))]?" } ] }, "questions": { "Q1.1": { "type": "choice", "instructions": "Answer the problem in `problems[0]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "Always True", "B": "Sometimes False" } }, "Q1.2": { "type": "choice", "instructions": "Answer the problem in `problems[1]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "Always True", "B": "Sometimes False" } } } }, "attempts": [ { "status": 200, "full_response_ms": 427.4284170005558, "raw_response": "{\"model\":\"jev-1.13.0\",\"answers\":{\"Q1.1\":{\"type\":\"choice\",\"choice\":\"A\",\"confidence\":0.97,\"probabilities\":{\"A\":0.98,\"B\":0.02}},\"Q1.2\":{\"type\":\"choice\",\"choice\":\"B\",\"confidence\":0.99,\"probabilities\":{\"A\":0.0,\"B\":1.0}}},\"usage\":{\"input_tokens\":588,\"output_tokens\":65}}" } ], "response": { "model": "jev-1.13.0", "answers": { "Q1.1": { "type": "choice", "choice": "A", "confidence": 0.97, "probabilities": { "A": 0.98, "B": 0.02 } }, "Q1.2": { "type": "choice", "choice": "B", "confidence": 0.99, "probabilities": { "A": 0.0, "B": 1.0 } } }, "usage": { "input_tokens": 588, "output_tokens": 65 } } }, { "section": 2, "request": { "model": "jev-1.13.0", "state": { "instructions": "Select the best answer for single-choice items and all correct options for select-all items. Mathematical expressions are exact; exp(x)=e^x. No calculator, external tools, retrieval, worked solutions or answer feedback. Answer each item from its stated context. All questions are independent API judgments; no previous correct answers are supplied.", "problems": [ { "id": "Q2.1", "context": "", "prompt": "For integers a,b, let d=gcd(a,b). Which argument proves that d divides ax+by for every pair of integers x,y?" }, { "id": "Q2.2", "context": "", "prompt": "7 divides 4^186 - 1. Hint: 186 = 31 * 6." }, { "id": "Q2.3", "context": "", "prompt": "5 divides 4^n - 1 for all even natural numbers n." }, { "id": "Q2.4", "context": "", "prompt": "What is the last digit (ones place) of 3^47?" }, { "id": "Q2.5", "context": "", "prompt": "Alice implements RSA correctly with N=33 and e=7 and sends ciphertext y=6. Given 33=3*11, what was the original message x?" }, { "id": "Q2.6", "context": "", "prompt": "Find (6^7 + 7^6) mod 91. Hint: use CRT; 91=7*13." } ] }, "questions": { "Q2.1": { "type": "choice", "instructions": "Answer the problem in `problems[0]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "Since d divides a and b, Bezout gives ax+by=d for every pair of integers x,y. Therefore ax+by is always equal to d and hence divisible by d.", "B": "Since d divides a and b, write d=ak and d=bj for integers k,j. Substituting gives ax+by=d(x/k+y/j), whose parenthesized term must be an integer.", "C": "Since d divides a and b, write a=dk and b=dj for integers k,j. Then ax+by=d(kx+jy), and kx+jy is an integer, establishing divisibility.", "D": "Since d is the greatest common divisor, every integer smaller than d divides both a and b. In particular x and y divide both, so d divides ax+by." } }, "Q2.2": { "type": "choice", "instructions": "Answer the problem in `problems[1]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "True", "B": "False" } }, "Q2.3": { "type": "choice", "instructions": "Answer the problem in `problems[2]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "True", "B": "False" } }, "Q2.4": { "type": "choice", "instructions": "Answer the problem in `problems[3]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "2", "B": "9", "C": "1", "D": "3", "E": "5", "F": "6", "G": "4", "H": "8", "I": "0", "J": "7" } }, "Q2.5": { "type": "choice", "instructions": "Answer the problem in `problems[4]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "15", "B": "27", "C": "18", "D": "6" } }, "Q2.6": { "type": "choice", "instructions": "Answer the problem in `problems[5]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "13", "B": "6", "C": "0", "D": "78" } } } }, "attempts": [ { "status": 200, "full_response_ms": 449.84275000024354, "raw_response": "{\"model\":\"jev-1.13.0\",\"answers\":{\"Q2.1\":{\"type\":\"choice\",\"choice\":\"C\",\"confidence\":1.0,\"probabilities\":{\"D\":0.0,\"B\":0.0,\"A\":0.0,\"C\":1.0}},\"Q2.2\":{\"type\":\"choice\",\"choice\":\"A\",\"confidence\":0.76,\"probabilities\":{\"B\":0.12,\"A\":0.88}},\"Q2.3\":{\"type\":\"choice\",\"choice\":\"A\",\"confidence\":0.66,\"probabilities\":{\"B\":0.17,\"A\":0.83}},\"Q2.4\":{\"type\":\"choice\",\"choice\":\"J\",\"confidence\":0.57,\"probabilities\":{\"D\":0.06,\"E\":0.02,\"G\":0.03,\"A\":0.11,\"C\":0.02,\"I\":0.0,\"J\":0.61,\"F\":0.03,\"B\":0.06,\"H\":0.06}},\"Q2.5\":{\"type\":\"choice\",\"choice\":\"D\",\"confidence\":0.13,\"probabilities\":{\"D\":0.35,\"B\":0.19,\"A\":0.19,\"C\":0.27}},\"Q2.6\":{\"type\":\"choice\",\"choice\":\"D\",\"confidence\":0.16,\"probabilities\":{\"D\":0.37,\"B\":0.26,\"A\":0.28,\"C\":0.09}}},\"usage\":{\"input_tokens\":1377,\"output_tokens\":287}}" } ], "response": { "model": "jev-1.13.0", "answers": { "Q2.1": { "type": "choice", "choice": "C", "confidence": 1.0, "probabilities": { "D": 0.0, "B": 0.0, "A": 0.0, "C": 1.0 } }, "Q2.2": { "type": "choice", "choice": "A", "confidence": 0.76, "probabilities": { "B": 0.12, "A": 0.88 } }, "Q2.3": { "type": "choice", "choice": "A", "confidence": 0.66, "probabilities": { "B": 0.17, "A": 0.83 } }, "Q2.4": { "type": "choice", "choice": "J", "confidence": 0.57, "probabilities": { "D": 0.06, "E": 0.02, "G": 0.03, "A": 0.11, "C": 0.02, "I": 0.0, "J": 0.61, "F": 0.03, "B": 0.06, "H": 0.06 } }, "Q2.5": { "type": "choice", "choice": "D", "confidence": 0.13, "probabilities": { "D": 0.35, "B": 0.19, "A": 0.19, "C": 0.27 } }, "Q2.6": { "type": "choice", "choice": "D", "confidence": 0.16, "probabilities": { "D": 0.37, "B": 0.26, "A": 0.28, "C": 0.09 } } }, "usage": { "input_tokens": 1377, "output_tokens": 287 } } }, { "section": 3, "request": { "model": "jev-1.13.0", "state": { "instructions": "Select the best answer for single-choice items and all correct options for select-all items. Mathematical expressions are exact; exp(x)=e^x. No calculator, external tools, retrieval, worked solutions or answer feedback. Answer each item from its stated context. All questions are independent API judgments; no previous correct answers are supplied.", "problems": [ { "id": "Q3.1", "context": "", "prompt": "Working modulo 6, how many distinct formal polynomials of degree exactly two are there?" }, { "id": "Q3.2", "context": "", "prompt": "Over GF(7), find g(x) of degree strictly less than 7, with coefficients in GF(7), giving the same output as f(x)=9x^66+7x^58+5x^55+5x^24+10x^19 for every x in GF(7). Hint: the solution is a simple polynomial." }, { "id": "Q3.3", "context": "", "prompt": "You receive n+2k points from a polynomial of degree n-1, with up to k corruptions. How many messages can you recover using Berlekamp-Welch?" } ] }, "questions": { "Q3.1": { "type": "choice", "instructions": "Answer the problem in `problems[0]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "125", "B": "180", "C": "216", "D": "150" } }, "Q3.2": { "type": "choice", "instructions": "Answer the problem in `problems[1]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "g(x)=x^6", "B": "g(x)=0", "C": "g(x)=1", "D": "g(x)=x" } }, "Q3.3": { "type": "choice", "instructions": "Answer the problem in `problems[2]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "k", "B": "n+2k", "C": "n", "D": "1" } } } }, "attempts": [ { "status": 200, "full_response_ms": 424.9754579996079, "raw_response": "{\"model\":\"jev-1.13.0\",\"answers\":{\"Q3.1\":{\"type\":\"choice\",\"choice\":\"B\",\"confidence\":0.28,\"probabilities\":{\"B\":0.45,\"C\":0.14,\"D\":0.34,\"A\":0.07}},\"Q3.2\":{\"type\":\"choice\",\"choice\":\"A\",\"confidence\":0.18,\"probabilities\":{\"B\":0.03,\"C\":0.22,\"D\":0.37,\"A\":0.38}},\"Q3.3\":{\"type\":\"choice\",\"choice\":\"D\",\"confidence\":0.83,\"probabilities\":{\"B\":0.03,\"C\":0.03,\"D\":0.88,\"A\":0.06}}},\"usage\":{\"input_tokens\":849,\"output_tokens\":138}}" } ], "response": { "model": "jev-1.13.0", "answers": { "Q3.1": { "type": "choice", "choice": "B", "confidence": 0.28, "probabilities": { "B": 0.45, "C": 0.14, "D": 0.34, "A": 0.07 } }, "Q3.2": { "type": "choice", "choice": "A", "confidence": 0.18, "probabilities": { "B": 0.03, "C": 0.22, "D": 0.37, "A": 0.38 } }, "Q3.3": { "type": "choice", "choice": "D", "confidence": 0.83, "probabilities": { "B": 0.03, "C": 0.03, "D": 0.88, "A": 0.06 } } }, "usage": { "input_tokens": 849, "output_tokens": 138 } } }, { "section": 4, "request": { "model": "jev-1.13.0", "state": { "instructions": "Select the best answer for single-choice items and all correct options for select-all items. Mathematical expressions are exact; exp(x)=e^x. No calculator, external tools, retrieval, worked solutions or answer feedback. Answer each item from its stated context. All questions are independent API judgments; no previous correct answers are supplied.", "problems": [ { "id": "Q4.1", "context": "", "prompt": "K_4 is planar." }, { "id": "Q4.2", "context": "", "prompt": "K_5 has an Eulerian tour." }, { "id": "Q4.3", "context": "", "prompt": "A 12-sided die is a planar graph wrapped around a sphere, with 12 faces and 20 vertices. How many edges does it have?" }, { "id": "Q4.4", "context": "", "prompt": "Which argument proves that, if a finite undirected graph has one odd-degree vertex, it must have another odd-degree vertex?" } ] }, "questions": { "Q4.1": { "type": "choice", "instructions": "Answer the problem in `problems[0]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "True", "B": "False" } }, "Q4.2": { "type": "choice", "instructions": "Answer the problem in `problems[1]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "True", "B": "False" } }, "Q4.3": { "type": "choice", "instructions": "Answer the problem in `problems[2]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "18", "B": "24", "C": "32", "D": "30" } }, "Q4.4": { "type": "choice", "instructions": "Answer the problem in `problems[3]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "The sum of degrees equals twice the number of edges, so it is even. If exactly one degree were odd and all others even, that sum would be odd, a contradiction.", "B": "Removing any odd-degree vertex leaves all remaining degrees even. Restoring it changes every remaining degree by one, so every other vertex then has odd degree.", "C": "An edge incident to the odd-degree vertex has another endpoint. That endpoint has odd degree because the common edge contributes one to both endpoint degrees.", "D": "The sum of degrees equals the number of edges, so it is even. If exactly one degree were odd and all others even, that sum would be odd, a contradiction." } } } }, "attempts": [ { "status": 200, "full_response_ms": 340.7250000000204, "raw_response": "{\"model\":\"jev-1.13.0\",\"answers\":{\"Q4.1\":{\"type\":\"choice\",\"choice\":\"A\",\"confidence\":0.12,\"probabilities\":{\"A\":0.56,\"B\":0.44}},\"Q4.2\":{\"type\":\"choice\",\"choice\":\"A\",\"confidence\":0.27,\"probabilities\":{\"A\":0.64,\"B\":0.36}},\"Q4.3\":{\"type\":\"choice\",\"choice\":\"D\",\"confidence\":0.96,\"probabilities\":{\"D\":0.97,\"C\":0.03,\"A\":0.0,\"B\":0.0}},\"Q4.4\":{\"type\":\"choice\",\"choice\":\"A\",\"confidence\":1.0,\"probabilities\":{\"D\":0.0,\"C\":0.0,\"A\":1.0,\"B\":0.0}}},\"usage\":{\"input_tokens\":965,\"output_tokens\":155}}" } ], "response": { "model": "jev-1.13.0", "answers": { "Q4.1": { "type": "choice", "choice": "A", "confidence": 0.12, "probabilities": { "A": 0.56, "B": 0.44 } }, "Q4.2": { "type": "choice", "choice": "A", "confidence": 0.27, "probabilities": { "A": 0.64, "B": 0.36 } }, "Q4.3": { "type": "choice", "choice": "D", "confidence": 0.96, "probabilities": { "D": 0.97, "C": 0.03, "A": 0.0, "B": 0.0 } }, "Q4.4": { "type": "choice", "choice": "A", "confidence": 1.0, "probabilities": { "D": 0.0, "C": 0.0, "A": 1.0, "B": 0.0 } } }, "usage": { "input_tokens": 965, "output_tokens": 155 } } }, { "section": 5, "request": { "model": "jev-1.13.0", "state": { "instructions": "Select the best answer for single-choice items and all correct options for select-all items. Mathematical expressions are exact; exp(x)=e^x. No calculator, external tools, retrieval, worked solutions or answer feedback. Answer each item from its stated context. All questions are independent API judgments; no previous correct answers are supplied.", "problems": [ { "id": "Q5.1", "context": "State whether each set is Finite, Countably Infinite, or Uncountably Infinite.", "prompt": "The set of all complex numbers." }, { "id": "Q5.2", "context": "State whether each set is Finite, Countably Infinite, or Uncountably Infinite.", "prompt": "The set of all prime numbers." }, { "id": "Q5.3", "context": "State whether each set is Finite, Countably Infinite, or Uncountably Infinite.", "prompt": "The real interval [0.001,0.1]." }, { "id": "Q5.4", "context": "State whether each set is Finite, Countably Infinite, or Uncountably Infinite.", "prompt": "The complex numbers a+bi where a,b are integers." }, { "id": "Q5.5", "context": "State whether each set is Finite, Countably Infinite, or Uncountably Infinite.", "prompt": "The set of edges of the complete bipartite graph K_(100,100)." }, { "id": "Q5.6", "context": "State whether each set is Finite, Countably Infinite, or Uncountably Infinite.", "prompt": "The set of all integer powers of 2." }, { "id": "Q5.7", "context": "State whether each set is Finite, Countably Infinite, or Uncountably Infinite.", "prompt": "The set of real polynomials of degree at most two passing through (1,1) and (2,2)." } ] }, "questions": { "Q5.1": { "type": "choice", "instructions": "Answer the problem in `problems[0]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "Finite", "B": "Countably Infinite", "C": "Uncountably Infinite" } }, "Q5.2": { "type": "choice", "instructions": "Answer the problem in `problems[1]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "Finite", "B": "Countably Infinite", "C": "Uncountably Infinite" } }, "Q5.3": { "type": "choice", "instructions": "Answer the problem in `problems[2]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "Finite", "B": "Countably Infinite", "C": "Uncountably Infinite" } }, "Q5.4": { "type": "choice", "instructions": "Answer the problem in `problems[3]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "Finite", "B": "Countably Infinite", "C": "Uncountably Infinite" } }, "Q5.5": { "type": "choice", "instructions": "Answer the problem in `problems[4]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "Finite", "B": "Countably Infinite", "C": "Uncountably Infinite" } }, "Q5.6": { "type": "choice", "instructions": "Answer the problem in `problems[5]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "Finite", "B": "Countably Infinite", "C": "Uncountably Infinite" } }, "Q5.7": { "type": "choice", "instructions": "Answer the problem in `problems[6]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "Finite", "B": "Countably Infinite", "C": "Uncountably Infinite" } } } }, "attempts": [ { "status": 200, "full_response_ms": 288.56083400023635, "raw_response": "{\"model\":\"jev-1.13.0\",\"answers\":{\"Q5.1\":{\"type\":\"choice\",\"choice\":\"C\",\"confidence\":1.0,\"probabilities\":{\"C\":1.0,\"B\":0.0,\"A\":0.0}},\"Q5.2\":{\"type\":\"choice\",\"choice\":\"B\",\"confidence\":1.0,\"probabilities\":{\"C\":0.0,\"B\":1.0,\"A\":0.0}},\"Q5.3\":{\"type\":\"choice\",\"choice\":\"C\",\"confidence\":1.0,\"probabilities\":{\"C\":1.0,\"B\":0.0,\"A\":0.0}},\"Q5.4\":{\"type\":\"choice\",\"choice\":\"B\",\"confidence\":1.0,\"probabilities\":{\"C\":0.0,\"B\":1.0,\"A\":0.0}},\"Q5.5\":{\"type\":\"choice\",\"choice\":\"A\",\"confidence\":0.97,\"probabilities\":{\"C\":0.0,\"B\":0.01,\"A\":0.99}},\"Q5.6\":{\"type\":\"choice\",\"choice\":\"B\",\"confidence\":1.0,\"probabilities\":{\"C\":0.0,\"B\":1.0,\"A\":0.0}},\"Q5.7\":{\"type\":\"choice\",\"choice\":\"C\",\"confidence\":0.46,\"probabilities\":{\"C\":0.64,\"B\":0.34,\"A\":0.02}}},\"usage\":{\"input_tokens\":1357,\"output_tokens\":269}}" } ], "response": { "model": "jev-1.13.0", "answers": { "Q5.1": { "type": "choice", "choice": "C", "confidence": 1.0, "probabilities": { "C": 1.0, "B": 0.0, "A": 0.0 } }, "Q5.2": { "type": "choice", "choice": "B", "confidence": 1.0, "probabilities": { "C": 0.0, "B": 1.0, "A": 0.0 } }, "Q5.3": { "type": "choice", "choice": "C", "confidence": 1.0, "probabilities": { "C": 1.0, "B": 0.0, "A": 0.0 } }, "Q5.4": { "type": "choice", "choice": "B", "confidence": 1.0, "probabilities": { "C": 0.0, "B": 1.0, "A": 0.0 } }, "Q5.5": { "type": "choice", "choice": "A", "confidence": 0.97, "probabilities": { "C": 0.0, "B": 0.01, "A": 0.99 } }, "Q5.6": { "type": "choice", "choice": "B", "confidence": 1.0, "probabilities": { "C": 0.0, "B": 1.0, "A": 0.0 } }, "Q5.7": { "type": "choice", "choice": "C", "confidence": 0.46, "probabilities": { "C": 0.64, "B": 0.34, "A": 0.02 } } }, "usage": { "input_tokens": 1357, "output_tokens": 269 } } }, { "section": 6, "request": { "model": "jev-1.13.0", "state": { "instructions": "Select the best answer for single-choice items and all correct options for select-all items. Mathematical expressions are exact; exp(x)=e^x. No calculator, external tools, retrieval, worked solutions or answer feedback. Answer each item from its stated context. All questions are independent API judgments; no previous correct answers are supplied.", "problems": [ { "id": "Q6", "context": "Two programs F and G are equivalent if, for every input, both halt with the same output or both do not halt. Suppose EQUIVALENT(F,G) always halts and returns TRUE iff F and G are equivalent. Complete HALT(P,x) to decide whether P halts on x:\ndef HALT(P,x):\n def F(y):\n ----(1)----\n ----(2)----\n def G(y):\n return 0\n return EQUIVALENT(----(3)----, ----(4)----)", "prompt": "Choose the ordered tuple filling blanks (1),(2),(3),(4)." } ] }, "questions": { "Q6": { "type": "choice", "instructions": "Answer the problem in `problems[0]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "(return 0; P(x); F; G)", "B": "(P(x); return 0; F; G)", "C": "(P(x); return 0; F; F)", "D": "(P(y); return 0; F; G)" } } } }, "attempts": [ { "status": 200, "full_response_ms": 461.1822500010021, "raw_response": "{\"model\":\"jev-1.13.0\",\"answers\":{\"Q6\":{\"type\":\"choice\",\"choice\":\"B\",\"confidence\":0.91,\"probabilities\":{\"B\":0.94,\"D\":0.04,\"A\":0.02,\"C\":0.0}}},\"usage\":{\"input_tokens\":620,\"output_tokens\":46}}" } ], "response": { "model": "jev-1.13.0", "answers": { "Q6": { "type": "choice", "choice": "B", "confidence": 0.91, "probabilities": { "B": 0.94, "D": 0.04, "A": 0.02, "C": 0.0 } } }, "usage": { "input_tokens": 620, "output_tokens": 46 } } }, { "section": 7, "request": { "model": "jev-1.13.0", "state": { "instructions": "Select the best answer for single-choice items and all correct options for select-all items. Mathematical expressions are exact; exp(x)=e^x. No calculator, external tools, retrieval, worked solutions or answer feedback. Answer each item from its stated context. All questions are independent API judgments; no previous correct answers are supplied.", "problems": [ { "id": "Q7.1", "context": "Answers may be unsimplified (binomial coefficients, factorials, exponents), but do not use summation or product notation. C(n,k) denotes a binomial coefficient.", "prompt": "A deck has 52 cards, 4 suits and 13 ranks per suit. A hand is an unordered set of five cards. How many hands contain exactly one 6 and exactly one 7?" }, { "id": "Q7.2", "context": "Answers may be unsimplified (binomial coefficients, factorials, exponents), but do not use summation or product notation. C(n,k) denotes a binomial coefficient.", "prompt": "Draw 3 cards without replacement. A means at least one ace. C_i means exactly i aces, for i=1,2,3. F,S,T mean respectively that the first, second or third card is an ace. Which representation of P(A) is easier, and why?" }, { "id": "Q7.3", "context": "Answers may be unsimplified (binomial coefficients, factorials, exponents), but do not use summation or product notation. C(n,k) denotes a binomial coefficient.\n\nAgnes distributes all 40 indistinguishable cookies among three distinct minions: Bob, Kevin and Stuart. Each has a carrying limit of 15 cookies.", "prompt": "With no carrying limit, how many distributions of the 40 cookies are possible?" }, { "id": "Q7.4", "context": "Answers may be unsimplified (binomial coefficients, factorials, exponents), but do not use summation or product notation. C(n,k) denotes a binomial coefficient.\n\nAgnes distributes all 40 indistinguishable cookies among three distinct minions: Bob, Kevin and Stuart. Each has a carrying limit of 15 cookies.", "prompt": "How many distributions exceed Bob's limit? Other minions may also exceed their limits." }, { "id": "Q7.5", "context": "Answers may be unsimplified (binomial coefficients, factorials, exponents), but do not use summation or product notation. C(n,k) denotes a binomial coefficient.\n\nAgnes distributes all 40 indistinguishable cookies among three distinct minions: Bob, Kevin and Stuart. Each has a carrying limit of 15 cookies.", "prompt": "How many distributions exceed both Bob's and Kevin's limits?" }, { "id": "Q7.6", "context": "Answers may be unsimplified (binomial coefficients, factorials, exponents), but do not use summation or product notation. C(n,k) denotes a binomial coefficient.\n\nAgnes distributes all 40 indistinguishable cookies among three distinct minions: Bob, Kevin and Stuart. Each has a carrying limit of 15 cookies. Here a counts unrestricted distributions; b counts distributions exceeding one specified limit; c counts distributions exceeding two specified limits.", "prompt": "Let a,b,c denote the answers to Q7.3,Q7.4,Q7.5 respectively. Express the number of distributions respecting all three limits in terms of a,b,c." } ] }, "questions": { "Q7.1": { "type": "choice", "instructions": "Answer the problem in `problems[0]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "C(4,2)*C(44,3)", "B": "4*4*C(50,3)", "C": "4*4*C(44,3)", "D": "4*4*C(44,3)*5!" } }, "Q7.2": { "type": "choice", "instructions": "Answer the problem in `problems[1]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "Use C_1,C_2,C_3: they are independent and their intersection is A, so their probabilities can be multiplied.", "B": "Use F,S,T: they are independent and their intersection is A, so their probabilities can be multiplied.", "C": "Use F,S,T: they are mutually exclusive and their union is A, so their probabilities can be added.", "D": "Use C_1,C_2,C_3: they are mutually exclusive and their union is A, so their probabilities can be added." } }, "Q7.3": { "type": "choice", "instructions": "Answer the problem in `problems[2]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "C(40,2)", "B": "3^40", "C": "C(42,2)", "D": "C(42,3)" } }, "Q7.4": { "type": "choice", "instructions": "Answer the problem in `problems[3]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "C(26,2)", "B": "C(27,2)", "C": "C(42,2)-C(26,2)", "D": "C(24,2)" } }, "Q7.5": { "type": "choice", "instructions": "Answer the problem in `problems[4]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "C(12,2)", "B": "C(10,2)", "C": "C(8,2)", "D": "C(26,2)^2" } }, "Q7.6": { "type": "choice", "instructions": "Answer the problem in `problems[5]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "a-b+c", "B": "a-3*b+6*c", "C": "a-3*b+3*c", "D": "a-3*b-3*c" } } } }, "attempts": [ { "status": 200, "full_response_ms": 317.04349999927217, "raw_response": "{\"model\":\"jev-1.13.0\",\"answers\":{\"Q7.1\":{\"type\":\"choice\",\"choice\":\"C\",\"confidence\":0.93,\"probabilities\":{\"D\":0.0,\"B\":0.05,\"C\":0.95,\"A\":0.0}},\"Q7.2\":{\"type\":\"choice\",\"choice\":\"D\",\"confidence\":0.99,\"probabilities\":{\"D\":1.0,\"B\":0.0,\"C\":0.0,\"A\":0.0}},\"Q7.3\":{\"type\":\"choice\",\"choice\":\"C\",\"confidence\":0.98,\"probabilities\":{\"C\":0.99,\"B\":0.0,\"A\":0.01,\"D\":0.0}},\"Q7.4\":{\"type\":\"choice\",\"choice\":\"A\",\"confidence\":0.37,\"probabilities\":{\"D\":0.16,\"A\":0.53,\"B\":0.27,\"C\":0.04}},\"Q7.5\":{\"type\":\"choice\",\"choice\":\"B\",\"confidence\":0.28,\"probabilities\":{\"C\":0.29,\"A\":0.24,\"D\":0.02,\"B\":0.45}},\"Q7.6\":{\"type\":\"choice\",\"choice\":\"C\",\"confidence\":0.96,\"probabilities\":{\"C\":0.97,\"B\":0.02,\"A\":0.01,\"D\":0.0}}},\"usage\":{\"input_tokens\":1861,\"output_tokens\":273}}" } ], "response": { "model": "jev-1.13.0", "answers": { "Q7.1": { "type": "choice", "choice": "C", "confidence": 0.93, "probabilities": { "D": 0.0, "B": 0.05, "C": 0.95, "A": 0.0 } }, "Q7.2": { "type": "choice", "choice": "D", "confidence": 0.99, "probabilities": { "D": 1.0, "B": 0.0, "C": 0.0, "A": 0.0 } }, "Q7.3": { "type": "choice", "choice": "C", "confidence": 0.98, "probabilities": { "C": 0.99, "B": 0.0, "A": 0.01, "D": 0.0 } }, "Q7.4": { "type": "choice", "choice": "A", "confidence": 0.37, "probabilities": { "D": 0.16, "A": 0.53, "B": 0.27, "C": 0.04 } }, "Q7.5": { "type": "choice", "choice": "B", "confidence": 0.28, "probabilities": { "C": 0.29, "A": 0.24, "D": 0.02, "B": 0.45 } }, "Q7.6": { "type": "choice", "choice": "C", "confidence": 0.96, "probabilities": { "C": 0.97, "B": 0.02, "A": 0.01, "D": 0.0 } } }, "usage": { "input_tokens": 1861, "output_tokens": 273 } } }, { "section": 8, "request": { "model": "jev-1.13.0", "state": { "instructions": "Select the best answer for single-choice items and all correct options for select-all items. Mathematical expressions are exact; exp(x)=e^x. No calculator, external tools, retrieval, worked solutions or answer feedback. Answer each item from its stated context. All questions are independent API judgments; no previous correct answers are supplied.", "problems": [ { "id": "Q8", "context": "", "prompt": "In a town, 3/4 of residents have black hair and 2/3 are female, independently. Two people are selected randomly with replacement. Given that at least one is a black-haired female, what is the probability both have black hair? Select the answer with valid supporting work. Hint: the answer is not 9/16." } ] }, "questions": { "Q8": { "type": "choice", "instructions": "Answer the problem in `problems[0]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "1/2: a randomly selected person is a black-haired female with probability (3/4)*(2/3)=1/2; replacement makes the requested conditional probability the same.", "B": "8/9: conditional on both people having black hair, the chance at least one is female is 1-(1/3)^2=8/9; this is the requested conditional probability.", "C": "3/4: if A means at least one black-haired female and B means both have black hair, then P(B|A)=P(B)/P(A)=(9/16)/(1-(1/2)^2)=3/4.", "D": "2/3: if A means at least one black-haired female and B means both have black hair, then P(B|A)=(9/16)*(1-(1/3)^2)/(1-(1/2)^2)=2/3." } } } }, "attempts": [ { "status": 200, "full_response_ms": 340.84749999965425, "raw_response": "{\"model\":\"jev-1.13.0\",\"answers\":{\"Q8\":{\"type\":\"choice\",\"choice\":\"C\",\"confidence\":0.56,\"probabilities\":{\"B\":0.07,\"C\":0.67,\"D\":0.23,\"A\":0.03}}},\"usage\":{\"input_tokens\":700,\"output_tokens\":46}}" } ], "response": { "model": "jev-1.13.0", "answers": { "Q8": { "type": "choice", "choice": "C", "confidence": 0.56, "probabilities": { "B": 0.07, "C": 0.67, "D": 0.23, "A": 0.03 } } }, "usage": { "input_tokens": 700, "output_tokens": 46 } } }, { "section": 9, "request": { "model": "jev-1.13.0", "state": { "instructions": "Select the best answer for single-choice items and all correct options for select-all items. Mathematical expressions are exact; exp(x)=e^x. No calculator, external tools, retrieval, worked solutions or answer feedback. Answer each item from its stated context. All questions are independent API judgments; no previous correct answers are supplied.", "problems": [ { "id": "Q9.2", "context": "Flip a biased coin independently infinitely many times, with heads probability p and tails probability 1-p. Give the distribution and parameters. The common discrete distributions named on the exam are Bernoulli, Binomial, Geometric, Uniform and Poisson. Original worked example Q9.1 (0 points): the indicator that the first three flips are heads is Bernoulli(p^3). Geometric(q) counts trials up to and including the first success (support 1,2,...).", "prompt": "Distribution of the number of heads in the first 70 flips?" }, { "id": "Q9.3", "context": "Flip a biased coin independently infinitely many times, with heads probability p and tails probability 1-p. Give the distribution and parameters. The common discrete distributions named on the exam are Bernoulli, Binomial, Geometric, Uniform and Poisson. Original worked example Q9.1 (0 points): the indicator that the first three flips are heads is Bernoulli(p^3). Geometric(q) counts trials up to and including the first success (support 1,2,...).", "prompt": "Conditional on exactly one head in the first 20 flips, what is the distribution of the flip number on which the first head occurs?" }, { "id": "Q9.4", "context": "Flip a biased coin independently infinitely many times, with heads probability p and tails probability 1-p. Give the distribution and parameters. The common discrete distributions named on the exam are Bernoulli, Binomial, Geometric, Uniform and Poisson. Original worked example Q9.1 (0 points): the indicator that the first three flips are heads is Bernoulli(p^3). Geometric(q) counts trials up to and including the first success (support 1,2,...).", "prompt": "Distribution of the gap between the first two tails, counting intervening heads? THHHT has gap 3. Hint: a standard random variable minus 1." }, { "id": "Q9.5", "context": "Flip a biased coin independently infinitely many times, with heads probability p and tails probability 1-p. Give the distribution and parameters. The common discrete distributions named on the exam are Bernoulli, Binomial, Geometric, Uniform and Poisson. Original worked example Q9.1 (0 points): the indicator that the first three flips are heads is Bernoulli(p^3). Geometric(q) counts trials up to and including the first success (support 1,2,...).", "prompt": "Let p=1/2. Distribution of the number of flips until the same outcome occurs twice consecutively? Hint: 1 plus a standard random variable." }, { "id": "Q9.6", "context": "Flip a biased coin independently infinitely many times, with heads probability p and tails probability 1-p. Give the distribution and parameters. The common discrete distributions named on the exam are Bernoulli, Binomial, Geometric, Uniform and Poisson. Original worked example Q9.1 (0 points): the indicator that the first three flips are heads is Bernoulli(p^3). Geometric(q) counts trials up to and including the first success (support 1,2,...).", "prompt": "Let p=1/2. Distribution of the number of runs in the first 50 flips? A run is an uninterrupted sequence of identical outcomes, e.g. HHHHHTTTHTTH begins with runs HHHHH, TTT, H, TT. Hint: 1 plus a standard random variable." } ] }, "questions": { "Q9.2": { "type": "choice", "instructions": "Answer the problem in `problems[0]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "Poisson(70*p)", "B": "Geometric(p)", "C": "Binomial(70,1-p)", "D": "Binomial(70,p)" } }, "Q9.3": { "type": "choice", "instructions": "Answer the problem in `problems[1]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "Geometric(p)", "B": "Uniform({1,2,...,20})", "C": "Binomial(20,p)", "D": "Uniform({0,1,...,19})" } }, "Q9.4": { "type": "choice", "instructions": "Answer the problem in `problems[2]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "Geometric(p)-1", "B": "Geometric(1-p)-1", "C": "Binomial(2,p)-1", "D": "Geometric(1-p)" } }, "Q9.5": { "type": "choice", "instructions": "Answer the problem in `problems[3]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "1+Geometric(1/2)", "B": "1+Binomial(2,1/2)", "C": "Geometric(1/2)", "D": "1+Geometric(1/4)" } }, "Q9.6": { "type": "choice", "instructions": "Answer the problem in `problems[4]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "1+Geometric(1/2)", "B": "1+Binomial(50,1/2)", "C": "1+Binomial(49,1/4)", "D": "1+Binomial(49,1/2)" } } } }, "attempts": [ { "status": 200, "full_response_ms": 447.7047920008772, "raw_response": "{\"model\":\"jev-1.13.0\",\"answers\":{\"Q9.2\":{\"type\":\"choice\",\"choice\":\"D\",\"confidence\":1.0,\"probabilities\":{\"D\":1.0,\"C\":0.0,\"B\":0.0,\"A\":0.0}},\"Q9.3\":{\"type\":\"choice\",\"choice\":\"B\",\"confidence\":0.96,\"probabilities\":{\"D\":0.02,\"C\":0.0,\"B\":0.98,\"A\":0.0}},\"Q9.4\":{\"type\":\"choice\",\"choice\":\"B\",\"confidence\":0.62,\"probabilities\":{\"D\":0.01,\"B\":0.71,\"A\":0.28,\"C\":0.0}},\"Q9.5\":{\"type\":\"choice\",\"choice\":\"A\",\"confidence\":0.73,\"probabilities\":{\"D\":0.09,\"C\":0.11,\"B\":0.0,\"A\":0.8}},\"Q9.6\":{\"type\":\"choice\",\"choice\":\"D\",\"confidence\":0.89,\"probabilities\":{\"D\":0.92,\"C\":0.01,\"B\":0.0,\"A\":0.07}}},\"usage\":{\"input_tokens\":1760,\"output_tokens\":228}}" } ], "response": { "model": "jev-1.13.0", "answers": { "Q9.2": { "type": "choice", "choice": "D", "confidence": 1.0, "probabilities": { "D": 1.0, "C": 0.0, "B": 0.0, "A": 0.0 } }, "Q9.3": { "type": "choice", "choice": "B", "confidence": 0.96, "probabilities": { "D": 0.02, "C": 0.0, "B": 0.98, "A": 0.0 } }, "Q9.4": { "type": "choice", "choice": "B", "confidence": 0.62, "probabilities": { "D": 0.01, "B": 0.71, "A": 0.28, "C": 0.0 } }, "Q9.5": { "type": "choice", "choice": "A", "confidence": 0.73, "probabilities": { "D": 0.09, "C": 0.11, "B": 0.0, "A": 0.8 } }, "Q9.6": { "type": "choice", "choice": "D", "confidence": 0.89, "probabilities": { "D": 0.92, "C": 0.01, "B": 0.0, "A": 0.07 } } }, "usage": { "input_tokens": 1760, "output_tokens": 228 } } }, { "section": 10, "request": { "model": "jev-1.13.0", "state": { "instructions": "Select the best answer for single-choice items and all correct options for select-all items. Mathematical expressions are exact; exp(x)=e^x. No calculator, external tools, retrieval, worked solutions or answer feedback. Answer each item from its stated context. All questions are independent API judgments; no previous correct answers are supplied.", "problems": [ { "id": "Q10", "context": "Each spin has four equally likely outcomes: alpha earns 1 point; beta earns 2 points; gamma gives two additional spins; delta loses 1 point and gives one additional spin. Start with one spin. Additional spins use the same rules. The score is the sum of points earned or lost. Example: alpha gives score 1. Example sequence delta,gamma,gamma,alpha,beta,alpha gives score -1+1+2+1=3.", "prompt": "Let X be the final score. What is E[X]?" } ] }, "questions": { "Q10": { "type": "choice", "instructions": "Answer the problem in `problems[0]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "0", "B": "1", "C": "2", "D": "3", "E": "4", "F": "infinity" } } } }, "attempts": [ { "status": 200, "full_response_ms": 410.32979100054945, "raw_response": "{\"model\":\"jev-1.13.0\",\"answers\":{\"Q10\":{\"type\":\"choice\",\"choice\":\"B\",\"confidence\":0.19,\"probabilities\":{\"E\":0.04,\"F\":0.16,\"A\":0.31,\"B\":0.32,\"C\":0.12,\"D\":0.05}}},\"usage\":{\"input_tokens\":587,\"output_tokens\":61}}" } ], "response": { "model": "jev-1.13.0", "answers": { "Q10": { "type": "choice", "choice": "B", "confidence": 0.19, "probabilities": { "E": 0.04, "F": 0.16, "A": 0.31, "B": 0.32, "C": 0.12, "D": 0.05 } } }, "usage": { "input_tokens": 587, "output_tokens": 61 } } }, { "section": 11, "request": { "model": "jev-1.13.0", "state": { "instructions": "Select the best answer for single-choice items and all correct options for select-all items. Mathematical expressions are exact; exp(x)=e^x. No calculator, external tools, retrieval, worked solutions or answer feedback. Answer each item from its stated context. All questions are independent API judgments; no previous correct answers are supplied.", "problems": [ { "id": "Q11.1", "context": "Normal(mu,v) denotes a normal distribution with mean mu and variance v. Poisson parameters are positive.", "prompt": "Independent X~Normal(1,2) and Y~Normal(2,1). What is the distribution of Z=2X-Y+1?" }, { "id": "Q11.2", "context": "Normal(mu,v) denotes a normal distribution with mean mu and variance v. Poisson parameters are positive.", "prompt": "Independent X,Y~Poisson(lambda). Let Z=X+Y. Select all true statements." }, { "id": "Q11.3", "context": "Normal(mu,v) denotes a normal distribution with mean mu and variance v. Poisson parameters are positive.", "prompt": "Let X_1,...,X_n be independent Poisson(lambda) variables and S=sum_i X_i. Select all true statements." } ] }, "questions": { "Q11.1": { "type": "choice", "instructions": "Answer the problem in `problems[0]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "Normal(1,5)", "B": "Normal(1,9)", "C": "Normal(1,3)", "D": "Normal(5,9)" } }, "Q11.2__A": { "type": "noul", "instructions": "Answer the problem in `problems[1]` using its context and the exam instructions. Is the following option true? Z~Poisson(2*lambda)" }, "Q11.2__B": { "type": "noul", "instructions": "Answer the problem in `problems[1]` using its context and the exam instructions. Is the following option true? Z has the distribution of 2P, where P~Poisson(lambda)" }, "Q11.2__C": { "type": "noul", "instructions": "Answer the problem in `problems[1]` using its context and the exam instructions. Is the following option true? None of the above Here \"None of the above\" means every substantive option is false. The substantive options are: {\"A\": \"Z~Poisson(2*lambda)\", \"B\": \"Z has the distribution of 2P, where P~Poisson(lambda)\"}" }, "Q11.3__A": { "type": "noul", "instructions": "Answer the problem in `problems[2]` using its context and the exam instructions. Is the following option true? For every n, S~Poisson(lambda*n)" }, "Q11.3__B": { "type": "noul", "instructions": "Answer the problem in `problems[2]` using its context and the exam instructions. Is the following option true? As n tends to infinity, (S-lambda*n)/sqrt(lambda*n) converges in distribution to Normal(0,1)" }, "Q11.3__C": { "type": "noul", "instructions": "Answer the problem in `problems[2]` using its context and the exam instructions. Is the following option true? None of the above Here \"None of the above\" means every substantive option is false. The substantive options are: {\"A\": \"For every n, S~Poisson(lambda*n)\", \"B\": \"As n tends to infinity, (S-lambda*n)/sqrt(lambda*n) converges in distribution to Normal(0,1)\"}" } } }, "attempts": [ { "status": 200, "full_response_ms": 400.96266599903174, "raw_response": "{\"model\":\"jev-1.13.0\",\"answers\":{\"Q11.1\":{\"type\":\"choice\",\"choice\":\"B\",\"confidence\":0.23,\"probabilities\":{\"C\":0.0,\"A\":0.41,\"B\":0.42,\"D\":0.17}},\"Q11.2__A\":{\"type\":\"noul\",\"noul\":0.97},\"Q11.2__B\":{\"type\":\"noul\",\"noul\":0.05},\"Q11.2__C\":{\"type\":\"noul\",\"noul\":0.12},\"Q11.3__A\":{\"type\":\"noul\",\"noul\":0.96},\"Q11.3__B\":{\"type\":\"noul\",\"noul\":0.97},\"Q11.3__C\":{\"type\":\"noul\",\"noul\":0.03}},\"usage\":{\"input_tokens\":1072,\"output_tokens\":182}}" } ], "response": { "model": "jev-1.13.0", "answers": { "Q11.1": { "type": "choice", "choice": "B", "confidence": 0.23, "probabilities": { "C": 0.0, "A": 0.41, "B": 0.42, "D": 0.17 } }, "Q11.2__A": { "type": "noul", "noul": 0.97 }, "Q11.2__B": { "type": "noul", "noul": 0.05 }, "Q11.2__C": { "type": "noul", "noul": 0.12 }, "Q11.3__A": { "type": "noul", "noul": 0.96 }, "Q11.3__B": { "type": "noul", "noul": 0.97 }, "Q11.3__C": { "type": "noul", "noul": 0.03 } }, "usage": { "input_tokens": 1072, "output_tokens": 182 } } }, { "section": 12, "request": { "model": "jev-1.13.0", "state": { "instructions": "Select the best answer for single-choice items and all correct options for select-all items. Mathematical expressions are exact; exp(x)=e^x. No calculator, external tools, retrieval, worked solutions or answer feedback. Answer each item from its stated context. All questions are independent API judgments; no previous correct answers are supplied.", "problems": [ { "id": "Q12.1", "context": "Student arrivals are modeled as a homogeneous Poisson process at a rate of one student per 30 minutes.", "prompt": "Nobody arrives during the first 50 minutes. What is the probability at least one student arrives during the final 10 minutes of the hour?" }, { "id": "Q12.2", "context": "Student arrivals are modeled as a homogeneous Poisson process at a rate of one student per 30 minutes.", "prompt": "At the same arrival rate, students never leave once they arrive. Starting from an empty room, what is the expected number at the end of one hour?" }, { "id": "Q12.3", "context": "Time between BART train departures is exponential, with a mean of 15 minutes.", "prompt": "Ishan arrives at a random time. What is his expected wait until a train departs?" }, { "id": "Q12.4", "context": "Time between BART train departures is exponential, with a mean of 15 minutes.", "prompt": "The station agent says the last train left 5 minutes ago. What is Ishan's expected remaining wait?" }, { "id": "Q12.5", "context": "", "prompt": "Trains and passengers have first arrival times A_t and A_p. The joint PDF is f(a_p,a_t)=lambda_p*lambda_t*exp(-lambda_p*a_p-lambda_t*a_t) for a_p,a_t>=0 and zero otherwise. Give an integral for P(A_t=1), clipped at 1?" }, { "id": "Q13.6", "context": "A 5 by 5 bingo card represents 25 booths. Melody visits each booth independently with probability p; its square is marked exactly when visited. There is no free square. The 12 possible bingo lines are 5 rows, 5 columns and 2 diagonals. X is the number of completely marked lines.", "prompt": "Assume E[X]<2. Which is the standard two-sided Chebyshev upper-bound expression applied to P(X>=2), in terms of E[X] and Var(X), clipped at 1?" } ] }, "questions": { "Q13.1": { "type": "choice", "instructions": "Answer the problem in `problems[0]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "p^25", "B": "12*p^5", "C": "12*p", "D": "25*p" } }, "Q13.2": { "type": "choice", "instructions": "Answer the problem in `problems[1]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "p^9", "B": "p^5", "C": "p^8", "D": "p^10" } }, "Q13.3": { "type": "choice", "instructions": "Answer the problem in `problems[2]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "p^10", "B": "p^9", "C": "p^25", "D": "2*p^5" } }, "Q13.4": { "type": "choice", "instructions": "Answer the problem in `problems[3]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "a+40*b+92*c-a^2", "B": "a+46*b+20*c-a^2", "C": "a+92*b+40*c", "D": "a+92*b+40*c-a^2" } }, "Q13.5": { "type": "choice", "instructions": "Answer the problem in `problems[4]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "1-(1-p^5)^12", "B": "min(1,12*p^5)", "C": "min(1,12*p^10)", "D": "min(1,p^5)" } }, "Q13.6": { "type": "choice", "instructions": "Answer the problem in `problems[5]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "min(1,(2-E[X])^2/Var(X))", "B": "min(1,Var(X)/(2-E[X]))", "C": "min(1,Var(X)/(2-E[X])^2)", "D": "min(1,Var(X)/(2+E[X])^2)" } } } }, "attempts": [ { "status": 200, "full_response_ms": 439.7859159998916, "raw_response": "{\"model\":\"jev-1.13.0\",\"answers\":{\"Q13.1\":{\"type\":\"choice\",\"choice\":\"B\",\"confidence\":1.0,\"probabilities\":{\"C\":0.0,\"A\":0.0,\"B\":1.0,\"D\":0.0}},\"Q13.2\":{\"type\":\"choice\",\"choice\":\"A\",\"confidence\":0.99,\"probabilities\":{\"C\":0.0,\"A\":1.0,\"B\":0.0,\"D\":0.0}},\"Q13.3\":{\"type\":\"choice\",\"choice\":\"A\",\"confidence\":0.99,\"probabilities\":{\"C\":0.0,\"A\":0.99,\"B\":0.01,\"D\":0.0}},\"Q13.4\":{\"type\":\"choice\",\"choice\":\"D\",\"confidence\":0.82,\"probabilities\":{\"C\":0.0,\"A\":0.1,\"B\":0.03,\"D\":0.87}},\"Q13.5\":{\"type\":\"choice\",\"choice\":\"B\",\"confidence\":1.0,\"probabilities\":{\"C\":0.0,\"A\":0.0,\"B\":1.0,\"D\":0.0}},\"Q13.6\":{\"type\":\"choice\",\"choice\":\"C\",\"confidence\":0.97,\"probabilities\":{\"C\":0.98,\"A\":0.01,\"B\":0.01,\"D\":0.0}}},\"usage\":{\"input_tokens\":1778,\"output_tokens\":279}}" } ], "response": { "model": "jev-1.13.0", "answers": { "Q13.1": { "type": "choice", "choice": "B", "confidence": 1.0, "probabilities": { "C": 0.0, "A": 0.0, "B": 1.0, "D": 0.0 } }, "Q13.2": { "type": "choice", "choice": "A", "confidence": 0.99, "probabilities": { "C": 0.0, "A": 1.0, "B": 0.0, "D": 0.0 } }, "Q13.3": { "type": "choice", "choice": "A", "confidence": 0.99, "probabilities": { "C": 0.0, "A": 0.99, "B": 0.01, "D": 0.0 } }, "Q13.4": { "type": "choice", "choice": "D", "confidence": 0.82, "probabilities": { "C": 0.0, "A": 0.1, "B": 0.03, "D": 0.87 } }, "Q13.5": { "type": "choice", "choice": "B", "confidence": 1.0, "probabilities": { "C": 0.0, "A": 0.0, "B": 1.0, "D": 0.0 } }, "Q13.6": { "type": "choice", "choice": "C", "confidence": 0.97, "probabilities": { "C": 0.98, "A": 0.01, "B": 0.01, "D": 0.0 } } }, "usage": { "input_tokens": 1778, "output_tokens": 279 } } }, { "section": 14, "request": { "model": "jev-1.13.0", "state": { "instructions": "Select the best answer for single-choice items and all correct options for select-all items. Mathematical expressions are exact; exp(x)=e^x. No calculator, external tools, retrieval, worked solutions or answer feedback. Answer each item from its stated context. All questions are independent API judgments; no previous correct answers are supplied.", "problems": [ { "id": "Q14", "context": "", "prompt": "Events A,B have nonzero probability and indicators I_A,I_B. Which argument proves that Cov(I_A,I_B)>0 implies P(A|B)>P(A)?" } ] }, "questions": { "Q14": { "type": "choice", "instructions": "Answer the problem in `problems[0]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "Cov(I_A,I_B)=P(A union B)-P(A)P(B)=P(B)[P(A|B)-P(A)]. Because P(B)>0, positive covariance forces the bracket to be positive.", "B": "Cov(I_A,I_B)=P(A intersection B)-P(A)P(B)=P(A)[P(A|B)-P(A)]. Because P(A)>0, positive covariance forces the bracket to be positive.", "C": "Cov(I_A,I_B)=P(A intersection B)-P(A)P(B)=P(B)[P(A|B)-P(A)]. Because P(B)>0, positive covariance forces the bracket to be positive.", "D": "Cov(I_A,I_B)=P(A)P(B)-P(A intersection B)=P(B)[P(A|B)-P(A)]. Because P(B)>0, positive covariance forces the bracket to be positive." } } } }, "attempts": [ { "status": 200, "full_response_ms": 384.9657089995162, "raw_response": "{\"model\":\"jev-1.13.0\",\"answers\":{\"Q14\":{\"type\":\"choice\",\"choice\":\"C\",\"confidence\":0.97,\"probabilities\":{\"A\":0.02,\"B\":0.0,\"C\":0.98,\"D\":0.0}}},\"usage\":{\"input_tokens\":655,\"output_tokens\":47}}" } ], "response": { "model": "jev-1.13.0", "answers": { "Q14": { "type": "choice", "choice": "C", "confidence": 0.97, "probabilities": { "A": 0.02, "B": 0.0, "C": 0.98, "D": 0.0 } } }, "usage": { "input_tokens": 655, "output_tokens": 47 } } }, { "section": 15, "request": { "model": "jev-1.13.0", "state": { "instructions": "Select the best answer for single-choice items and all correct options for select-all items. Mathematical expressions are exact; exp(x)=e^x. No calculator, external tools, retrieval, worked solutions or answer feedback. Answer each item from its stated context. All questions are independent API judgments; no previous correct answers are supplied.", "problems": [ { "id": "Q15.1", "context": "Gaussian(mu,v) denotes a Gaussian distribution with mean mu and variance v.", "prompt": "Let X~Gaussian(3,6) and Y~Exponential(3) be independent. What is P(X=Y)?" }, { "id": "Q15.2", "context": "Gaussian(mu,v) denotes a Gaussian distribution with mean mu and variance v.", "prompt": "For X~Gaussian(3,6), which statement is true about P(X<4)?" }, { "id": "Q15.3", "context": "Gaussian(mu,v) denotes a Gaussian distribution with mean mu and variance v.\n\nA, B and C are independent Uniform(0,12) random variables. X indicates that C lies between A and B.", "prompt": "What is P(X=1 | A,B), in terms of A and B?" }, { "id": "Q15.4", "context": "Gaussian(mu,v) denotes a Gaussian distribution with mean mu and variance v.\n\nA, B and C are independent Uniform(0,12) random variables. X indicates that C lies between A and B.", "prompt": "Without conditioning on A,B, what is P(X=1)? Hint: there is a way without integrals." }, { "id": "Q15.5", "context": "Gaussian(mu,v) denotes a Gaussian distribution with mean mu and variance v.\n\nA, B and C are independent Uniform(0,12) random variables. X indicates that C lies between A and B. Q15.3 asks for P(X=1 | A,B); Q15.4 asks for P(X=1).", "prompt": "What is E[abs(A-B)]? Hint: use the previous two parts to avoid integrals. The original exam labels this particularly challenging." } ] }, "questions": { "Q15.1": { "type": "choice", "instructions": "Answer the problem in `problems[0]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "0", "B": "Cannot be determined from the stated information", "C": "1", "D": "1/2" } }, "Q15.2": { "type": "choice", "instructions": "Answer the problem in `problems[1]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "<0.5", "B": "=0.5", "C": ">0.5", "D": "Not enough information" } }, "Q15.3": { "type": "choice", "instructions": "Answer the problem in `problems[2]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "1-abs(A-B)/12", "B": "abs(A-B)/12", "C": "(A-B)/12", "D": "abs(A-B)/144" } }, "Q15.4": { "type": "choice", "instructions": "Answer the problem in `problems[3]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "1/2", "B": "1/6", "C": "2/3", "D": "1/3" } }, "Q15.5": { "type": "choice", "instructions": "Answer the problem in `problems[4]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "0", "B": "4", "C": "8", "D": "6" } } } }, "attempts": [ { "status": 200, "full_response_ms": 377.990958000737, "raw_response": "{\"model\":\"jev-1.13.0\",\"answers\":{\"Q15.1\":{\"type\":\"choice\",\"choice\":\"A\",\"confidence\":0.99,\"probabilities\":{\"B\":0.0,\"D\":0.0,\"A\":1.0,\"C\":0.0}},\"Q15.2\":{\"type\":\"choice\",\"choice\":\"C\",\"confidence\":0.38,\"probabilities\":{\"B\":0.02,\"D\":0.02,\"C\":0.54,\"A\":0.42}},\"Q15.3\":{\"type\":\"choice\",\"choice\":\"B\",\"confidence\":0.96,\"probabilities\":{\"B\":0.97,\"D\":0.0,\"C\":0.0,\"A\":0.03}},\"Q15.4\":{\"type\":\"choice\",\"choice\":\"D\",\"confidence\":0.96,\"probabilities\":{\"B\":0.01,\"D\":0.96,\"C\":0.01,\"A\":0.02}},\"Q15.5\":{\"type\":\"choice\",\"choice\":\"C\",\"confidence\":0.35,\"probabilities\":{\"B\":0.45,\"D\":0.03,\"C\":0.52,\"A\":0.0}}},\"usage\":{\"input_tokens\":1288,\"output_tokens\":233}}" } ], "response": { "model": "jev-1.13.0", "answers": { "Q15.1": { "type": "choice", "choice": "A", "confidence": 0.99, "probabilities": { "B": 0.0, "D": 0.0, "A": 1.0, "C": 0.0 } }, "Q15.2": { "type": "choice", "choice": "C", "confidence": 0.38, "probabilities": { "B": 0.02, "D": 0.02, "C": 0.54, "A": 0.42 } }, "Q15.3": { "type": "choice", "choice": "B", "confidence": 0.96, "probabilities": { "B": 0.97, "D": 0.0, "C": 0.0, "A": 0.03 } }, "Q15.4": { "type": "choice", "choice": "D", "confidence": 0.96, "probabilities": { "B": 0.01, "D": 0.96, "C": 0.01, "A": 0.02 } }, "Q15.5": { "type": "choice", "choice": "C", "confidence": 0.35, "probabilities": { "B": 0.45, "D": 0.03, "C": 0.52, "A": 0.0 } } }, "usage": { "input_tokens": 1288, "output_tokens": 233 } } }, { "section": 16, "request": { "model": "jev-1.13.0", "state": { "instructions": "Select the best answer for single-choice items and all correct options for select-all items. Mathematical expressions are exact; exp(x)=e^x. No calculator, external tools, retrieval, worked solutions or answer feedback. Answer each item from its stated context. All questions are independent API judgments; no previous correct answers are supplied.", "problems": [ { "id": "Q16.1", "context": "Tom travels from Chicago (CHI) to Miami (MIA). Each outgoing train route is equally likely. The diagram, transcribed without solving: CHI -> SFO (1/3), DC (1/3), NYC (1/3); SFO -> CHI (1); DC -> SFO (1/3), NYC (1/3), MIA (1/3); NYC -> CHI (1/2), DC (1/2); MIA -> MIA (1).", "prompt": "Find the probability of reaching MIA from CHI before visiting NYC. Select a system of equations, without solving it. h(s) denotes the probability of reaching MIA before NYC starting at s; the requested probability is h(CHI)." }, { "id": "Q16.2", "context": "Tom travels from Chicago (CHI) to Miami (MIA). Each outgoing train route is equally likely. The diagram, transcribed without solving: CHI -> SFO (1/3), DC (1/3), NYC (1/3); SFO -> CHI (1); DC -> SFO (1/3), NYC (1/3), MIA (1/3); NYC -> CHI (1/2), DC (1/2); MIA -> MIA (1).", "prompt": "Tom spends 3 days on each visit to NYC and 1 day in every other city before departing. Travel takes zero days. Select equations for the expected days to first arrival at MIA, starting in CHI and including its initial day. Do not solve. t(s) denotes the remaining expected days starting at s." } ] }, "questions": { "Q16.1": { "type": "choice", "instructions": "Answer the problem in `problems[0]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "h(MIA)=1; h(NYC)=0; h(SFO)=h(CHI); h(DC)=(h(SFO)+h(NYC)+h(MIA))/3; h(CHI)=(h(SFO)+h(DC))/2.", "B": "h(MIA)=1; h(NYC)=0; h(SFO)=h(CHI); h(DC)=(h(NYC)+h(MIA))/2; h(CHI)=(h(SFO)+h(DC)+h(NYC))/3.", "C": "h(MIA)=0; h(NYC)=1; h(SFO)=h(CHI); h(DC)=(h(SFO)+h(NYC)+h(MIA))/3; h(CHI)=(h(SFO)+h(DC)+h(NYC))/3.", "D": "h(MIA)=1; h(NYC)=0; h(SFO)=h(CHI); h(DC)=(h(SFO)+h(NYC)+h(MIA))/3; h(CHI)=(h(SFO)+h(DC)+h(NYC))/3." } }, "Q16.2": { "type": "choice", "instructions": "Answer the problem in `problems[1]` using its context and the exam instructions. Select the best complete answer.", "criteria": { "A": "t(MIA)=0; t(SFO)=1+t(CHI); t(CHI)=1+(t(SFO)+t(DC)+t(NYC))/3; t(DC)=1+(t(NYC)+t(MIA))/3; t(NYC)=3+(t(CHI)+t(DC))/2.", "B": "t(MIA)=0; t(SFO)=1+t(CHI); t(CHI)=1+(t(SFO)+t(DC)+t(NYC))/3; t(DC)=1+(t(SFO)+t(NYC)+t(MIA))/3; t(NYC)=3+(t(CHI)+t(DC))/2.", "C": "t(MIA)=0; t(SFO)=1+t(CHI); t(CHI)=1+(t(SFO)+t(DC)+t(NYC))/3; t(DC)=1+(t(SFO)+t(NYC)+t(MIA))/3; t(NYC)=1+(t(CHI)+t(DC))/2.", "D": "t(MIA)=1; t(SFO)=1+t(CHI); t(CHI)=1+(t(SFO)+t(DC)+t(NYC))/3; t(DC)=1+(t(SFO)+t(NYC)+t(MIA))/3; t(NYC)=3+(t(CHI)+t(DC))/2." } } } }, "attempts": [ { "status": 200, "full_response_ms": 336.481874999663, "raw_response": "{\"model\":\"jev-1.13.0\",\"answers\":{\"Q16.1\":{\"type\":\"choice\",\"choice\":\"D\",\"confidence\":0.98,\"probabilities\":{\"B\":0.0,\"D\":0.99,\"C\":0.0,\"A\":0.01}},\"Q16.2\":{\"type\":\"choice\",\"choice\":\"B\",\"confidence\":0.97,\"probabilities\":{\"B\":0.97,\"D\":0.02,\"A\":0.01,\"C\":0.0}}},\"usage\":{\"input_tokens\":1392,\"output_tokens\":95}}" } ], "response": { "model": "jev-1.13.0", "answers": { "Q16.1": { "type": "choice", "choice": "D", "confidence": 0.98, "probabilities": { "B": 0.0, "D": 0.99, "C": 0.0, "A": 0.01 } }, "Q16.2": { "type": "choice", "choice": "B", "confidence": 0.97, "probabilities": { "B": 0.97, "D": 0.02, "A": 0.01, "C": 0.0 } } }, "usage": { "input_tokens": 1392, "output_tokens": 95 } } } ], "elapsed_seconds": 6.179232874999798 }, "scores": { "correct_items": 52, "total_items": 58, "accuracy": 0.896551724137931, "invalid_or_missing_items": 0, "adapted_weighted_points": 129.0, "adapted_weighted_possible": 154.0, "weighting_note": "Q12 weights are 12/5 each by evaluator convention, not an original published subpart rubric. No partial credit. This is not an original-exam grade.", "source_format_preserved": { "correct": 16, "items": 17 }, "adapted_free_response": { "correct": 36, "items": 41 }, "repaired_items": { "correct": 7, "items": 7 }, "unrepaired_items": { "correct": 45, "items": 51 }, "items": [ { "id": "Q1.1", "correct": true, "valid_response": true, "selected": [ "A" ], "expected": [ "A" ], "adapted_weight": 2, "repairs": [] }, { "id": "Q1.2", "correct": true, "valid_response": true, "selected": [ "B" ], "expected": [ "B" ], "adapted_weight": 2, "repairs": [] }, { "id": "Q2.1", "correct": true, "valid_response": true, "selected": [ "C" ], "expected": [ "C" ], "adapted_weight": 5, "repairs": [] }, { "id": "Q2.2", "correct": true, "valid_response": true, "selected": [ "A" ], "expected": [ "A" ], "adapted_weight": 2, "repairs": [] }, { "id": "Q2.3", "correct": true, "valid_response": true, "selected": [ "A" ], "expected": [ "A" ], "adapted_weight": 2, "repairs": [] }, { "id": "Q2.4", "correct": true, "valid_response": true, "selected": [ "J" ], "expected": [ "J" ], "adapted_weight": 3, "repairs": [] }, { "id": "Q2.5", "correct": false, "valid_response": true, "selected": [ "D" ], "expected": [ "C" ], "adapted_weight": 3, "repairs": [] }, { "id": "Q2.6", "correct": false, "valid_response": true, "selected": [ "D" ], "expected": [ "B" ], "adapted_weight": 4, "repairs": [] }, { "id": "Q3.1", "correct": true, "valid_response": true, "selected": [ "B" ], "expected": [ "B" ], "adapted_weight": 3, "repairs": [ "formal_polynomials" ] }, { "id": "Q3.2", "correct": false, "valid_response": true, "selected": [ "A" ], "expected": [ "D" ], "adapted_weight": 3, "repairs": [] }, { "id": "Q3.3", "correct": true, "valid_response": true, "selected": [ "D" ], "expected": [ "D" ], "adapted_weight": 3, "repairs": [] }, { "id": "Q4.1", "correct": true, "valid_response": true, "selected": [ "A" ], "expected": [ "A" ], "adapted_weight": 2, "repairs": [] }, { "id": "Q4.2", "correct": true, "valid_response": true, "selected": [ "A" ], "expected": [ "A" ], "adapted_weight": 2, "repairs": [] }, { "id": "Q4.3", "correct": true, "valid_response": true, "selected": [ "D" ], "expected": [ "D" ], "adapted_weight": 2, "repairs": [] }, { "id": "Q4.4", "correct": true, "valid_response": true, "selected": [ "A" ], "expected": [ "A" ], "adapted_weight": 4, "repairs": [] }, { "id": "Q5.1", "correct": true, "valid_response": true, "selected": [ "C" ], "expected": [ "C" ], "adapted_weight": 1, "repairs": [] }, { "id": "Q5.2", "correct": true, "valid_response": true, "selected": [ "B" ], "expected": [ "B" ], "adapted_weight": 1, "repairs": [] }, { "id": "Q5.3", "correct": true, "valid_response": true, "selected": [ "C" ], "expected": [ "C" ], "adapted_weight": 1, "repairs": [] }, { "id": "Q5.4", "correct": true, "valid_response": true, "selected": [ "B" ], "expected": [ "B" ], "adapted_weight": 1, "repairs": [] }, { "id": "Q5.5", "correct": true, "valid_response": true, "selected": [ "A" ], "expected": [ "A" ], "adapted_weight": 1, "repairs": [] }, { "id": "Q5.6", "correct": true, "valid_response": true, "selected": [ "B" ], "expected": [ "B" ], "adapted_weight": 1, "repairs": [] }, { "id": "Q5.7", "correct": true, "valid_response": true, "selected": [ "C" ], "expected": [ "C" ], "adapted_weight": 1, "repairs": [] }, { "id": "Q6", "correct": true, "valid_response": true, "selected": [ "B" ], "expected": [ "B" ], "adapted_weight": 4, "repairs": [] }, { "id": "Q7.1", "correct": true, "valid_response": true, "selected": [ "C" ], "expected": [ "C" ], "adapted_weight": 3, "repairs": [] }, { "id": "Q7.2", "correct": true, "valid_response": true, "selected": [ "D" ], "expected": [ "D" ], "adapted_weight": 3, "repairs": [] }, { "id": "Q7.3", "correct": true, "valid_response": true, "selected": [ "C" ], "expected": [ "C" ], "adapted_weight": 3, "repairs": [] }, { "id": "Q7.4", "correct": true, "valid_response": true, "selected": [ "A" ], "expected": [ "A" ], "adapted_weight": 3, "repairs": [] }, { "id": "Q7.5", "correct": true, "valid_response": true, "selected": [ "B" ], "expected": [ "B" ], "adapted_weight": 2, "repairs": [] }, { "id": "Q7.6", "correct": true, "valid_response": true, "selected": [ "C" ], "expected": [ "C" ], "adapted_weight": 4, "repairs": [] }, { "id": "Q8", "correct": false, "valid_response": true, "selected": [ "C" ], "expected": [ "D" ], "adapted_weight": 7, "repairs": [] }, { "id": "Q9.2", "correct": true, "valid_response": true, "selected": [ "D" ], "expected": [ "D" ], "adapted_weight": 2, "repairs": [] }, { "id": "Q9.3", "correct": true, "valid_response": true, "selected": [ "B" ], "expected": [ "B" ], "adapted_weight": 2, "repairs": [] }, { "id": "Q9.4", "correct": true, "valid_response": true, "selected": [ "B" ], "expected": [ "B" ], "adapted_weight": 3, "repairs": [] }, { "id": "Q9.5", "correct": true, "valid_response": true, "selected": [ "A" ], "expected": [ "A" ], "adapted_weight": 3, "repairs": [] }, { "id": "Q9.6", "correct": true, "valid_response": true, "selected": [ "D" ], "expected": [ "D" ], "adapted_weight": 3, "repairs": [] }, { "id": "Q10", "correct": false, "valid_response": true, "selected": [ "B" ], "expected": [ "C" ], "adapted_weight": 3, "repairs": [] }, { "id": "Q11.1", "correct": true, "valid_response": true, "selected": [ "B" ], "expected": [ "B" ], "adapted_weight": 3, "repairs": [] }, { "id": "Q11.2", "correct": true, "valid_response": true, "selected": [ "A" ], "expected": [ "A" ], "adapted_weight": 2, "repairs": [] }, { "id": "Q11.3", "correct": true, "valid_response": true, "selected": [ "A", "B" ], "expected": [ "A", "B" ], "adapted_weight": 2, "repairs": [ "positive_poisson_rate" ] }, { "id": "Q12.1", "correct": true, "valid_response": true, "selected": [ "B" ], "expected": [ "B" ], "adapted_weight": 2.4, "repairs": [ "poisson_process" ] }, { "id": "Q12.2", "correct": true, "valid_response": true, "selected": [ "B" ], "expected": [ "B" ], "adapted_weight": 2.4, "repairs": [ "poisson_process" ] }, { "id": "Q12.3", "correct": true, "valid_response": true, "selected": [ "B" ], "expected": [ "B" ], "adapted_weight": 2.4, "repairs": [] }, { "id": "Q12.4", "correct": true, "valid_response": true, "selected": [ "A" ], "expected": [ "A" ], "adapted_weight": 2.4, "repairs": [] }, { "id": "Q12.5", "correct": true, "valid_response": true, "selected": [ "B" ], "expected": [ "B" ], "adapted_weight": 2.4, "repairs": [] }, { "id": "Q13.1", "correct": true, "valid_response": true, "selected": [ "B" ], "expected": [ "B" ], "adapted_weight": 3, "repairs": [] }, { "id": "Q13.2", "correct": true, "valid_response": true, "selected": [ "A" ], "expected": [ "A" ], "adapted_weight": 2, "repairs": [] }, { "id": "Q13.3", "correct": true, "valid_response": true, "selected": [ "A" ], "expected": [ "A" ], "adapted_weight": 2, "repairs": [] }, { "id": "Q13.4", "correct": true, "valid_response": true, "selected": [ "D" ], "expected": [ "D" ], "adapted_weight": 5, "repairs": [] }, { "id": "Q13.5", "correct": true, "valid_response": true, "selected": [ "B" ], "expected": [ "B" ], "adapted_weight": 2, "repairs": [] }, { "id": "Q13.6", "correct": true, "valid_response": true, "selected": [ "C" ], "expected": [ "C" ], "adapted_weight": 3, "repairs": [ "chebyshev_condition" ] }, { "id": "Q14", "correct": true, "valid_response": true, "selected": [ "C" ], "expected": [ "C" ], "adapted_weight": 5, "repairs": [] }, { "id": "Q15.1", "correct": true, "valid_response": true, "selected": [ "A" ], "expected": [ "A" ], "adapted_weight": 2, "repairs": [ "independence_added" ] }, { "id": "Q15.2", "correct": true, "valid_response": true, "selected": [ "C" ], "expected": [ "C" ], "adapted_weight": 2, "repairs": [] }, { "id": "Q15.3", "correct": true, "valid_response": true, "selected": [ "B" ], "expected": [ "B" ], "adapted_weight": 2, "repairs": [] }, { "id": "Q15.4", "correct": true, "valid_response": true, "selected": [ "D" ], "expected": [ "D" ], "adapted_weight": 2, "repairs": [] }, { "id": "Q15.5", "correct": false, "valid_response": true, "selected": [ "C" ], "expected": [ "B" ], "adapted_weight": 5, "repairs": [] }, { "id": "Q16.1", "correct": true, "valid_response": true, "selected": [ "D" ], "expected": [ "D" ], "adapted_weight": 3, "repairs": [] }, { "id": "Q16.2", "correct": true, "valid_response": true, "selected": [ "B" ], "expected": [ "B" ], "adapted_weight": 3, "repairs": [ "dc_edge_in_key" ] } ] } }