Question: Let X and Y be independent binomial random variables with parameters (n, p1) and (m, p2), respectively. (a) Find E (X/n Y/n) (b) Find

Let X and Y be independent binomial random variables with parameters (n, p1) and (m, p2), respectively.
(a) Find E (X/n – Y/n)
(b) Find Var (X/n – Y/n)
(c) Show that (x/n – Y/n) ~ N (E(Y/n – Y/n), Var (X/n – Y/n)), for largest n.

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