(b) Let Fo, Fi, F2 and F3 denote the sample frequencies of 0, 1, 2 and 3, respectively. That is, F = C_i-1(X; k) for k = 0, 1, 2, 3. Find the likelihood function in terms of Fo, Fi, F2 and F3. Show that the maximum likelihood estimator (MLE) of 0 is 0 = 1 - Fo ln.
Hint: Use the fact that Fo + Fi + F2 + F3 = n.
(iii) Find the sampling distribution of Fo. Is 0 unbiased for 0? Explain why or why not. Find the variance of 0. Find an approximate 95% confidence interval for 0 based on 0.