GATE Engineering Mathematics: Probability and Statistics – Previous Year Questions
25 GATE previous year questions on Probability and Statistics (Engineering Mathematics, Computer Science) with answers and explanations, from every paper.
- GATE 2017 CS Q29 – Let X be a Gaussian random variable with mean 0 and variance 2. Let Y = (X, 0) where (a, b) is the maximum of a and b. The median of Y is .
- GATE 2016 CS Q14 – A probability density function on the interval [a, 1] is given by 1/x2 and outside this interval the value of the function is zero. The value of a is…
- GATE 2016 CS Q39 – Consider the following experiment. Step 1. Flip a fair coin twice. Step 2. If the outcomes are (TAILS, HEADS) then output Y and stop. Step 3. If the…
- GATE 2018 CS Q25 – Two people, P and Q, decide to independently roll two identical dice, each with 6 faces, numbered 1 to 6. The person with the lower number wins. In…
- GATE 2018 CS Q54 – Consider Guwahati (G) and Delhi (D) whose temperatures can be classified as high (H), medium (M) and low (L). Let P(H G) denote the probability that…
- GATE 2019 CS Q32 – Two numbers are chosen independently and uniformly at random from the set \1,2,,13\. The probability (rounded off to 3 decimal places) that their…
- GATE 2019 CS Q57 – Suppose Y is distributed uniformly in the open interval (1,6). The probability that the polynomial 3x2+6xY+3Y+6 has only real roots is (rounded off to…
- GATE 2026 CS (CS2) Q14 – The probability density function f(x) of a random variable X is f(x) = 132 (-x218), x (-,+). Which one of the following statements is correct about…
- GATE 2026 CS (CS2) Q63 – Suppose an unbiased coin is tossed 6 times. Each toss is independent. Let E 1 be the event that among the second, fourth, and sixth tosses, there are…
- GATE 2026 CS (CS1) Q11 – An urn contains one red ball and one blue ball. At each step, a ball is picked uniformly at random from the urn, and this ball together with another…
- GATE 2026 CS (CS1) Q58 – Let X be a random variable which takes values in the set \1, 2, 3, 4, 5, 6, 7, 8\. Further, (X = 1) = (X = 2) = (X = 5) = (X = 7) = 16 and (X = 3) =…
- GATE 2025 CS (CS2) Q64 – A quadratic polynomial (x - )(x - ) over complex numbers is said to be square invariant if (x - )(x - ) = (x - 2)(x - 2). Suppose from the set of all…
- GATE 2025 CS (CS2) Q65 – The unit interval (0,1) is divided at a point chosen uniformly distributed over (0,1) in R into two disjoint subintervals. The expected length of the…
- GATE 2025 CS (CS1) Q32 – A box contains 5 coins: 4 regular coins and 1 fake coin. When a regular coin is tossed, the probability P(head) = 0.5 and for a fake coin, P(head) =…
- GATE 2025 CS (CS1) Q56 – Suppose a 5-bit message is transmitted from a source to a destination through a noisy channel. The probability that a bit of the message gets flipped…
- GATE 2024 CS (CS2) Q18 – When six unbiased dice are rolled simultaneously, the probability of getting all distinct numbers (i.e., 1, 2, 3, 4, 5, and 6) is
- GATE 2024 CS (CS2) Q44 – Let x and y be random variables, not necessarily independent, that take real values in the interval [0,1]. Let z=xy and let the mean values of x,y,z…
- GATE 2024 CS (CS1) Q14 – Consider a permutation sampled uniformly at random from the set of all permutations of \1,2,3,,n\ for some n 4. Let X be the event that 1 occurs…
- GATE 2024 CS (CS1) Q27 – Let A and B be two events in a probability space with P(A)=0.3, P(B)=0.5, and P(A B)=0.1. Which of the following statements is/are TRUE?
- GATE 2024 CS (CS1) Q63 – A bag contains 10 red balls and 15 blue balls. Two balls are drawn randomly without replacement. Given that the first ball drawn is red, the…
- GATE 2023 CS Q53 – Consider a random experiment where two fair coins are tossed. Let A be the event that denotes HEAD on both the throws, B be the event that denotes…
- GATE 2021 CS Q28 – The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter 2.…
- GATE 2021 CS Q45 – Consider the two statements. S 1: There exist random variables X and Y such that (E[(X-E(X))(Y-E(Y))])2 > Var[X]Var[Y] S 2: For all random variables X…
- GATE 2021 CS Q64 – A sender (S) transmits a signal, which can be one of the two kinds: H and L with probabilities 0.1 and 0.9 respectively, to a receiver (R). In the…
- GATE 2020 CS Q55 – For n>2, let a\0,1\n be a non-zero vector. Suppose that x is chosen uniformly at random from \0,1\n. Then, the probability that i=1na ix i is an odd…