GATE 2025 ST – Question 33

Estimation · Unbiased and Minimum Variance Estimation · 1 mark · Numerical answer

Five observations are iid N(θ,6),θ∈ℝ. Let c(θ) be the Cramér–Rao variance bound for unbiased estimation of θ. Find 15inf_(θ∈ℝ)c(θ) (integer).

Show answer and explanation

Correct answer: 18 to 18

Explanation

Information per observation is 1/6, giving total 5/6. Thus the bound is c(θ)=6/5, constant in θ. Multiplying by 15 gives **18**.

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