GATE 2026 ST – Question 29

Standard Univariate Distributions · Continuous Distributions · 1 mark · Numerical answer

Independent X₁,X₂,X₃ have densities ke^(−kx),x>0, for k=1,2,3 respectively. For Y=min(X₁,X₂,X₃), find E(3Y²−Y) (integer).

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Correct answer: 0 to 0

Explanation

The independent survival probabilities multiply to e^(−(1+2+3)y), so Y is exponential of rate 6. E(Y)=1/6 and E(Y²)=2/6²=1/18. Therefore 3/18−1/6=**0**.

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