91Ó°ÊÓ

If \(X\) is normally distributed with mean 1 and variance 4 , use the tables to find \(P\\{2

For the multinomial distribution (Exercise 17), let \(N_{i}\) denote the number of times outcome \(i\) occurs. Find (i) \(E\left[N_{i}\right]\) (ii) \(\operatorname{Var}\left(N_{i}\right)\) (iii) \(\operatorname{Cov}\left(N_{i}, N_{j}\right)\) (iv) Compute the expected number of outcomes that do not occur.

Let \(X\) and \(Y\) be independent normal random variables, each having parameters \(\mu\) and \(\sigma^{2}\). Show that \(X+Y\) is independent of \(X-Y\).