GATE 2024 ST – Question 32

Joint Distributions · Order Statistics · 1 mark · Numerical answer

Three iid observations have density 2x on (0,1),zero otherwise. Find P(min(X₁,X₂,X₃)≥E X₁) to two decimals.

Show answer and explanation

Correct answer: 0.15 to 0.19

Explanation

E X=∫₀¹2x²dx=2/3 and F(x)=x² on [0,1]. Each observation exceeds 2/3 with probability 1−4/9=5/9. Independence gives (5/9)³=125/729≈**.17**.

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