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?

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?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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

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