GATE 2026 ST – Question 28

Joint Distributions · Joint and Conditional Distributions · 1 mark · Numerical answer

X,Y have joint density x+y on 0<x<1,0<y<1, zero otherwise. Find 72[Var(X)+Var(Y)] (integer).

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Correct answer: 11 to 11

Explanation

The marginals are identical with f_X(x)=x+1/2. E(X)=1/3+1/4=7/12, and E(X²)=1/4+1/6=5/12. Thus Var(X)=5/12−49/144=11/144, the same for Y. The result is 72×22/144=**11**.

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