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 live helmets examined is flawed?
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The maximum likelihood estimator and bias are investigated and discussed in the solution. The solution is detailed and well presented.