A random sample ofnbike helmets manufactured by a certain company is selected. LetX= the number among thenthat are flawed, and letp=P(flawed). Assume that onlyXis observed, rather than the sequence ofS's andF's.

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 = Pttlawed). Assume that only X is observed. rather than the sequence at 8'5 and F's. (a) Derive the maximum likelihood estimator 0t p. (Use x for x and n for n as necessary.) It n = 22 and x = 7'. what is the estimate? [Give answer accurate to 3 decimal places.) (b) Is the estimator of part {a} unbiased '? 0 yes Ono (c) If n = 22 and x = 7. what is the mle of the probability (1 - p)5 that none of the next ve helmets examined is flawed? [Give answer accurate to 3 decimal places.)