20. A random sample of n bike helmets manufactured by a certain company is selected. Let X
the number among the n that are flawed, and let p
P(flawed). Assume that only X is observed, rather than the sequence of S’s and F’s.

a. Derive the maximum likelihood estimator of p. If n
20 and x
3, what is the estimate?

b. Is the estimator of part

(a) unbiased?

c. If n
20 and x
3, what is the mle of the probability

(1  p)5 that none of the next five helmets examined is flawed?