GATE 2024 ST – Question 19

Standard Univariate Distributions · Continuous Distributions · 1 mark · Multiple choice

X has beta density Γ(α+β)x^(α−1)(1−x)^(β−1)/[Γ(α)Γ(β)] on (0,1),α,β>0. If E X=1/3,E X²=1/6, find α+3β.

Show answer and explanation

Correct answer: (A) 7

Explanation

The first moment gives β=2α. The second becomes α(α+1)/[3α(3α+1)]=1/6, implying 2(α+1)=3α+1 and α=1. Then β=2 and α+3β=**7, A**.

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