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Math Help - Maxiumum Likelihood estimator

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    Maxiumum Likelihood estimator

    A sample of n items is examined from each large batch of a mass produced article. The number of good items in a sample has binomial distribution with parameters n,p. The batch is accepted if all n items are good and rejected otherwise. Out of m batches x are accepted and m-x are rejected. Find max likelihood estimator for p.
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    Quote Originally Posted by scubasteve123 View Post
    A sample of n items is examined from each large batch of a mass produced article. The number of good items in a sample has binomial distribution with parameters n,p. The batch is accepted if all n items are good and rejected otherwise. Out of m batches x are accepted and m-x are rejected. Find max likelihood estimator for p.
    Start by introducing some notation:

    Let Y be the random variable 'number of good items in a batch'. Then Y ~ Binomial(n, p).
    Pr(batch rejected) = 1 - \Pr(Y = n) = 1 - p^n.

    Let X be the random variable 'number of batches rejected'. Then X ~ Binomial (m, 1 - p^n).

    Now construct the likelihood function etc.
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