GATE 2022 ST – Question 35

Non-parametric Statistics · Empirical Distribution and Goodness of Fit · 1 mark · Numerical answer

Eight iid observations have density x/8 on 0<x<4,zero elsewhere. If α=Var[F₈(2)] for their empirical CDF,find 128α as an integer.

Show answer and explanation

Correct answer: 3 to 3

Explanation

P(X≤2)=∫₀²x/8 dx=1/4. The empirical CDF at 2 is the mean of eight iid Bernoulli(1/4) indicators,so α=(1/4)(3/4)/8=3/128. Hence **128α=3**.

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