A random sample of n bike helmets manufactured by a 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 Ss and Fs. (a) Derive the maximum likelihood estimator of p. If n= 20 and x = 3 what is the estimate?
(b) Is the estimator of (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?