A random sample X1;X2; ;X3 of size n is taken from a Poisson distribution with a mean of , 0 < < 1. (a) Show that the maximum likelihood estimator for is X .
(b) Let X equal the number of aws per feet of a used computer tape. Assume that X has a Poisson distribution with a mean of . If 40 observations of X yielded 5 zeros, 7 ones, 12 twos, 9 threes, 5 fours, 1 ve, and 1 six, nd the maximum likelihood estimator of .