Let X 1 ,X 2 , ,X n be a random sample from a Poisson distribution with mean Thus, Y n i 1 X i has a Poisson distribution with mean n Moreover, X Y n is approximately N(, n) for large n Show that u(Y n) Y n is a function of Y n whose variance is essentially free of

Question: Let X 1 ,X 2 , . . .,X n be a random sample from a Poisson distribution with mean . Thus, Y =

Let X₁,X₂, . . .,X_n be a random sample from a Poisson distribution with mean μ. Thus, Y = Σⁿ_i=1 X_i 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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