GATE 2021 ST – Question 27
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.
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Show answer and explanation
Correct answer: 7 to 7
Explanation
The kth order density is proportional to x^(k−1)(2−x)^(8−k). Match exponents:k−1=6 and 8−k=1,both giving **k=7**. Its coefficient 8!/(6!1!2⁸)=7/32 confirms normalization.