Home › Previous year questions › GATE 2023 ST › Question 22GATE 2023 ST – Question 22 Estimation · Point Estimation and Consistency · 1 mark · Multiple choice
X has exponential density e^(−x/λ)/λ for x>0,λ>0 unknown. Y₁,…,Y_n are iid with the distribution of X² and Ȳ is their mean. Which is the method-of-moments estimator of λ?
√(Ȳ/2) √Ȳ (1/2)√Ȳ 2√Ȳ Practise this question in The GATE Grind →
Show answer and explanation Correct answer: (A) √(Ȳ/2)
Explanation The first Y moment is E Y=E X²=2λ². Equate this to Ȳ and take the positive root,obtaining **√(Ȳ/2), A**.
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