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Competitive Stats
Q14Section I (Objective (Q1–Q80))14 of 80

Statistical Inference — sample mean attaining the Cramer-Rao bound

Consider the following statements: I. Xi∼N(θ,σ2)X_i \sim N(\theta, \sigma^2); σ2\sigma^2 known and θ\theta unknown; i=1,2,3,…,ni = 1, 2, 3, …, n. II. Xi∼X_i \sim Bernoulli(θ)(\theta); θ\theta unknown; i=1,2,3,…,ni = 1, 2, 3, …, n. The variance of sample mean coincides with the Cramer-Rao lower bound for every θ\theta, for

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