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GATE 2022 ST – Question 62

Joint Distributions · Order Statistics · 2 marks · Numerical answer

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.

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Correct answer: 8 to 8

Explanation

Each observation lies on either side of μ with probability 1/2. Failure occurs if all observations are below μ or all above,probability 2(1/2)^n. Thus 1−2^(1−n)≥.99 requires 2^(n−1)≥100. Since 2⁶=64 and 2⁷=128,the smallest n is **8**.

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