GATE 2026 ST – Question 15

Joint Distributions · Joint and Conditional Distributions · 1 mark · Multiple choice

Identically distributed X,Y have variance σ²∈(0,∞). Their correlation coefficient is which expression?

Show answer and explanation

Correct answer: (A) 1−E[(X−Y)²]/(2σ²)

Explanation

Equal distributions give equal means, so E[(X−Y)²]=Var(X−Y)=2σ²−2Cov(X,Y). Divide by 2σ² and rearrange to obtain **A**. Independence was not assumed.

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