GATE Standard Univariate Distributions: Continuous Distributions – Previous Year Questions
12 GATE previous year questions on Continuous Distributions (Standard Univariate Distributions, Statistics) with answers and explanations, from every paper.
- GATE 2022 ST Q25 – X,Y are independent exponential variables with E X²=1/2 and E Y²=2/9. Find P(X<2Y) to two decimals.
- GATE 2023 ST Q16 – X has density αλ x(α−1) exp(−λxα) for x>0,zero otherwise,α,λ>0. Its median is 1 and third quartile is 2. Find (α,λ).
- GATE 2023 ST Q18 – X has gamma density λα x(α−1)e(−λx)/Γ(α),x>0,α,λ>0. Which claim is NOT true?
- GATE 2023 ST Q37 – X has density 1/x² for x≥1,zero otherwise. For Y=ln X,find P(Y<1 Y<2).
- GATE 2024 ST Q19 – X has beta density Γ(α+β)x(α−1)(1−x)(β−1)/[Γ(α)Γ(β)] on (0,1),α,β>0. If E X=1/3,E X²=1/6, find α+3β.
- GATE 2024 ST Q40 – Checkout service times are independent exponential with density e(−x/10)/10,x≥0. On arrival one customer is already being served and has spent five…
- GATE 2024 ST Q42 – The X i are iid N(μ,σ²). I:if [√5/(σ(2n+1))]Σᵢ₌₁ⁿi(X i−μ) is N(0,1), then n=2. II:E[−ln Φ((X₁−μ)/σ)]³=6. Which hold?
- GATE 2025 ST Q40 – X>0 has lognormal density f(x)=( x2)-1[-12(( x-)/)2]. If ln(E(X²)/(E X)²)=4, find Var(ln X).
- GATE 2025 ST Q59 – Service densities at pumps P₁,P₂ are λe(−λx) and λ²xe(−λx),x>0. Each pump is selected with probability 1/2. If the chance of service exceeding one…
- GATE 2026 ST Q16 – Independent identically distributed normal X,Y satisfy P(X+2Y≤3)=P(2X−Y≥4). Find E(X).
- GATE 2026 ST Q29 – Independent X₁,X₂,X₃ have densities ke(−kx),x>0, for k=1,2,3 respectively. For Y=min(X₁,X₂,X₃), find E(3Y²−Y) (integer).
- GATE 2026 ST Q62 – For X~N(3,1), find E[X⁴(X−3)] (integer).