GATE Standard Univariate Distributions: Discrete Distributions – Previous Year Questions

11 GATE previous year questions on Discrete Distributions (Standard Univariate Distributions, Statistics) with answers and explanations, from every paper.

1. GATE 2021 ST Q41 (2 marks, Multiple choice) – X is Poisson with E X²=110. Which claim is NOT true?
2. GATE 2022 ST Q26 (1 mark, Numerical answer) – X has PMF P(X=x)=(3/4)(x−1)/4,x=1,2,… . Evaluate Σ from n=0 to ∞ of P(n<X≤n+3),to two decimals.
3. GATE 2023 ST Q17 (1 mark, Multiple choice) – If X is Poisson with mean λ>0,find E[1/(X+1) X>0].
4. GATE 2023 ST Q20 (1 mark, Multiple choice) – Each of five boxes contains 3 blue,1 red and 2 black pens. Independently draw one pen uniformly from each box. If X₁ counts blue pens and X₂ counts…
5. GATE 2023 ST Q54 (2 marks, Multiple select) – X has PMF P(X=0)=(1+e⁻¹)/2 and P(X=k)=e⁻¹/(2k!) for k≥1. Which hold?
6. GATE 2024 ST Q31 (1 mark, Numerical answer) – X~Poisson(λ),λ>0, satisfies P(X=4)=2P(X=5). If P(X=α) is its maximum mass, find α (integer).
7. GATE 2024 ST Q41 (2 marks, Multiple choice) – X is discrete uniform on 1,3,5,…,99. Find E(X X is not a multiple of 15).
8. GATE 2025 ST Q14 (1 mark, Multiple choice) – For X~Poisson(ln2), find E[e((ln3)X)].
9. GATE 2025 ST Q29 (1 mark, Numerical answer) – For X~Binomial(2,1/3), find 18E(X²) (integer).
10. GATE 2026 ST Q27 (1 mark, Numerical answer) – For n≥7, X has probabilities P(X=i)=2P(X=i−1),i=2,…,n, summing to 1 over i=1,…,n. Find (2ⁿ−1)P(X=7) (integer).
11. GATE 2026 ST Q42 (2 marks, Multiple choice) – X has support 0,1,2,… and P(X≥k+1 X≥k)=p for every k≥0,0<p<1. Which holds?