GATE Joint Distributions: Order Statistics – Previous Year Questions
7 GATE previous year questions on Order Statistics (Joint Distributions, Statistics) with answers and explanations, from every paper.
- GATE 2021 ST Q27 – The kth order statistic from a size-eight Uniform(0,2) sample has density (7/32)x⁶(2−x) for 0<x<2,zero otherwise. Find k.
- GATE 2021 ST Q48 – X (1)<⋯<X (5) are order statistics of a size-five Uniform(0,θ) sample. P:3X (2) is unbiased for θ. Q:Var[E(2X (3) X (5))]≤Var(2X (3)). Which hold?
- GATE 2021 ST Q58 – X n are iid Uniform(0,3). Independently,Y has PMF P(Y=k)=1/[(e−1)k!],k=1,2,… . Find P(maxX₁,…,X Y≤1),to two decimals.
- GATE 2022 ST Q53 – Three iid observations have density 2x on (0,1),zero elsewhere. Let p be the probability the maximum is at least twice the minimum. Find p to three…
- GATE 2022 ST Q62 – Y₁<⋯<Y n are order statistics of an iid sample from a continuous distribution symmetric about its mean μ. Find the smallest n with P(Y₁<μ<Y n)≥.99.
- GATE 2024 ST Q32 – Three iid observations have density 2x on (0,1),zero otherwise. Find P(min(X₁,X₂,X₃)≥E X₁) to two decimals.
- GATE 2025 ST Q44 – Independent X,Y₁,Y₂ have exponential rates 2,1,1 respectively. R i is the ascending rank of Y i among the three observations. Find E(R₁+R₂).