GATE 2022 ST – Question 55

Estimation · Unbiased and Minimum Variance Estimation · 2 marks · Numerical answer

The Poisson(θ) sample is 0,1,1,2,0. If α is the minimum-variance unbiased estimate of P(X≤1),find 5⁴α as an integer.

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Correct answer: 512 to 512

Explanation

T=ΣX_i is complete sufficient and observed T=4. Rao–Blackwellize the unbiased indicator 1{X₁≤1}:given T=4,X₁∼Binomial(4,1/5). Thus α=(4/5)⁴+4(1/5)(4/5)³=(256+256)/625. Multiplying by 5⁴ gives **512**.

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