Question:
Let x1, .., xn be a random sample from a (geometric) distribution with discrete density function fx(x) pq x , x=0,1, 2,.,. Where q=(1-p)
(a) Find the maximum likelihood estimator (MLE) of p
(b) Let ?=1/p. What is the MLE of ? ?
(c) It can be shown that E(X)=q/p and Var (x) = q/p2. Use these facts to show that the MLE of ? in (b) is a best estimator in that it is an unbiased estimator of ? with minimum variance.
What is the asymptomatic (large n) distribution of the MLE of ?