GATE 2025 ST – Question 44

Joint Distributions · Order Statistics · 2 marks · Multiple choice

Independent X,Y₁,Y₂ have exponential rates 2,1,1 respectively. R_i is the ascending rank of Y_i among the three observations. Find E(R₁+R₂).

13/3
22/5
21/5
9/2

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Correct answer: (A) 13/3

Explanation

The three ranks sum to 6. The rank of X is 1+1_(Y₁<X)+1_(Y₂<X), with each comparison probability 1/(1+2)=1/3. Thus E rank X=5/3, giving E(R₁+R₂)=6−5/3=**13/3, A**.

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