GATE 2021 ST – Question 58

Joint Distributions · Order Statistics · 2 marks · Numerical answer

X_n are iid Uniform(0,3). Independently,Y has PMF P(Y=k)=1/[(e−1)k!],k=1,2,… . Find P(max{X₁,…,X_Y}≤1),to two decimals.

Show answer and explanation

Correct answer: 0.20 to 0.26

Explanation

Given Y=k,the probability is (1/3)^k. Average over Y:Σ_(k≥1)(1/3)^k/[(e−1)k!]=(e^(1/3)−1)/(e−1)≈**0.23**.

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