Let X1, . . . , Xn, . . . ∼ iid Poisson(λ). (a) Using the Central Limit Theorem, find a limiting distribution for x̄n. (b) We wish to estimate √λ, the standard deviation of the Poisson distribution. Find a limiting distribution for √x̄n   (c) Is √x̄n an asymptotically efficient estimator?

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 Let X1, . . . , Xn, . . . ∼ iid Poisson(λ).
(a) Using the Central Limit Theorem, find a limiting distribution for x̄n.
(b) We wish to estimate √λ, the standard deviation of the Poisson distribution. Find a limiting distribution for √x̄n  
(c) Is √x̄n an asymptotically efficient estimator?

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