16. Define MLEs for the following problems:

(a) Estimating the pi 0

s based on a random sample from a multinomial population distribution.

(b) Estimating the unknown parameters in the mean vector m and covariance matrix S based on a random sample from a bivariate normal distribution.

(c) Estimating b in the population distribution f xð Þ ; b ¼ 2x b exp  x2 b

Ið0;1Þ ðxÞ

(d) Estimating the parameter p in a negative binomial population distribution where r is known.