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