GATE 2021 ST – Question 13

Estimation · Point Estimation and Consistency · 1 mark · Multiple choice

An iid sample of size n≥2 has density exp[−(x−θ)/θ]/θ for x>θ,zero otherwise,θ>0. Find the method-of-moments estimator of θ.

Show answer and explanation

Correct answer: (A) ΣX_i/(2n)

Explanation

Write X=θ+E with E exponential of mean θ. Thus E X=2θ. Equate the sample mean to 2θ to obtain θ̂=X̄/2=**A**.

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