# Thread: Maxiumum Likelihood estimator

1. ## 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.

2. Originally Posted by scubasteve123
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.