The GATE Grind

GATE Probability and Statistics: Random variables, discrete and continuous distributions – Previous Year Questions

13 GATE previous year questions on Random variables, discrete and continuous distributions (Probability and Statistics, Data Science and Artificial Intelligence) with answers and explanations, from every paper.

  1. GATE 2024 DA Q11 (1 mark, Multiple choice) – Consider the following statements: (i) The mean and variance of a Poisson random variable are equal. (ii) For a standard normal random variable, the…
  2. GATE 2024 DA Q56 (2 marks, Numerical answer) – Let X be a random variable uniformly distributed in the interval [1, 3] and Y be a random variable uniformly distributed in the interval [2, 4]. If X…
  3. GATE 2024 DA Q57 (2 marks, Numerical answer) – Let X be a random variable exponentially distributed with parameter > 0. The probability density function of X is given by: f X(x) = e- x for x 0 and…
  4. GATE 2025 DA Q19 (1 mark, Multiple choice) – Let X be a continuous random variable whose cumulative distribution function (CDF) F X(x), for some t, is given as follows: F X(x) = cases 0 & x t \\…
  5. GATE 2025 DA Q21 (1 mark, Multiple choice) – It is given that P(X 2) = 0.25 for an exponentially distributed random variable X with E[X] = 1, where E[X] denotes the expectation of X. What is the…
  6. GATE 2025 DA Q36 (2 marks, Multiple choice) – Let Y = Z2, Z = X - , where X is a normal random variable with mean and variance 2. The variance of Y is
  7. GATE 2025 DA Q39 (2 marks, Multiple choice) – Consider the cumulative distribution function (CDF) of a random variable X: F X(x) = cases 0 & x -1 \\ 14(x + 1)2 & -1 x 1 \\ 1 & x 1 cases The value…
  8. GATE 2025 DA Q41 (2 marks, Multiple choice) – For x R, the floor function is denoted by f(x) = x and defined as follows x = k, k x < k + 1, where k is an integer. Let Y = X , where X is an…
  9. GATE 2025 DA Q61 (2 marks, Numerical answer) – A bag contains 5 white balls and 10 black balls. In a random experiment, n balls are drawn from the bag one at a time with replacement. Let S n denote…
  10. GATE 2026 DA Q28 (1 mark, Multiple select) – Suppose a random variable Z follows Normal( = 0, 2 = 1) distribution with probability density function g(z) and cumulative distribution function G(z).…
  11. GATE 2026 DA Q34 (1 mark, Numerical answer) – Let X be an exponentially distributed random variable with mean \ (> 0). If P(X > 5) = 0.35, then the conditional probability P(X > 10 X > 5) is .…
  12. GATE 2026 DA Q53 (2 marks, Multiple select) – Let X 1, X 2, , X n be n independent random variables. Each of the random variables follows Normal( = 0, 2 = 1) distribution. Define X = 1n i=1n X i.…
  13. GATE 2026 DA Q54 (2 marks, Multiple select) – Let X be a discrete valued random variable with cumulative distribution function F(x). Which of the following statements is/are correct?