The sample sum S is gamma with shape 21,rate λ. The likelihood gives λ̂=21/S, and E(1/S)=λ/(21−1)=λ/20. Thus Eλ̂=21λ/20 and bias=λ/20, so α=1/20 and **1/α=20**.
More Point Estimation and Consistency questions
GATE 2024 ST Q24– An iid sample n≥2 has density θ(2x)(θ−1) on 0<x≤1/2 and θ(2−2x)(θ−1) on 1/2<x≤1,zero…
GATE 2024 ST Q44– Independent X n~Poisson(λ+2(−n)),λ>0 unknown. Which holds?
GATE 2024 ST Q62– A Poisson process N(t) of unknown rate λ counts road potholes up to distance t km.…
GATE 2023 ST Q22– X has exponential density e(−x/λ)/λ for x>0,λ>0 unknown. Y₁,…,Y n are iid with the…
GATE 2023 ST Q23– An iid sample of size n≥2 has density f(x;θ)=2(−ln x) exp[−(ln x)²/θ]/(θx) on 0<x<1,zero…
GATE 2023 ST Q39– An iid sample of size n has density exp[−(x−μ)] for x≥μ,zero otherwise,μ unknown. Let M̂…