GATE 2023 ST – Question 17

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

If X is Poisson with mean λ>0,find E[1/(X+1) | X>0].

Show answer and explanation

Correct answer: (A) [1−e^(−λ)−λe^(−λ)]/[λ(1−e^(−λ))]

Explanation

Summing λ^k/[k!(k+1)] gives E[1/(X+1)]=(1−e^(−λ))/λ. Subtract the k=0 contribution e^(−λ),then divide by P(X>0)=1−e^(−λ). This yields **A**.

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