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Let X1, . . . , Xn be independent and identically distributed random variables with Xi NBin(r, p) for each i. Given positive integer r,

Let X1, . . . , Xn be independent and identically distributed random variables with Xi NBin(r, p) for each i. Given positive integer r, find a maximum likelihood estimator for p and determine whether it is biased.

To investigate bias, use Jensen's inequality.

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