Let X 1 ,X 2 , . . .,X n be a random sample from a Poisson

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Let X1,X2, . . .,Xn be a random sample from a Poisson distribution with mean μ. Thus, Y = Σni=1 Xi has a Poisson distribution with mean nμ. Moreover, ‾X = Y/n is approximately N(μ, μ/n) for large n. Show that u(Y/n) =Y/n is a function of Y/n whose variance is essentially free of μ.

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Introduction To Mathematical Statistics

ISBN: 9780321794710

7th Edition

Authors: Robert V., Joseph W. McKean, Allen T. Craig

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