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a) Let Xi for i = 1,2,...n be random variables with E[Xi] = μi (not necessarily...

a) Let Xi for i = 1,2,...n be random variables with E[Xi] = μi (not necessarily independent). Show that E[∑ni =1 Xi] = [∑ni =1 μi]. Show from Definition

b) Suppose that random variables Yi for i = 1, 2,...,n are independent and identically distributed withE[Yi] =γ(gamma) and Var[Yi] = σ2, Use part (a) to show that E[Ybar] =γ(gamma).

(c) Suppose that random variables Yi for i = 1, 2,...,n are independent and identically distributed with E[Yi] =γ(gamma) and Var[Yi] = σ2. Show that Var[Ybar] =σ2/n. (recall E[(∑ni=1Yi)2] = Var[∑ni=1Yi] + E[∑ni=1Yi]2

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