GATE 2023 ST – Question 40

Estimation · Point Estimation and Consistency · 2 marks · Multiple choice

X₁,…,X₁₀ are iid N(0,θ²),θ>0. Set T=ΣX_i²/10. For c>0,the MSE of cT as an estimator of θ² is minimized at c₀. Find c₀.

Show answer and explanation

Correct answer: (A) 5/6

Explanation

E T=θ² and Var T=2θ⁴/10=θ⁴/5. MSE(cT)=θ⁴[c²/5+(c−1)²]. Differentiate to obtain 2c/5+2(c−1)=0,so c₀=**5/6, A**.

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