Question: Let X 1 , , X n be a random sample from a population with mean and variance 2 . Show that E n (

Let X1,,Xn be a random sample from a population with mean and variance 2 . Show that

En(Xn)=0 and Varn(Xn)=1.

Thus, the normalization of Xn in the Central Limit Theorem gives random variables that have the same mean and variance as the limiting n(0,1) distribution.

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