Question: Let X be a binomial random variable with parameters (n, p). What value of p maximizes P{X = k}, k = 0, 1, . .

Let X be a binomial random variable with parameters (n, p). What value of p maximizes P{X = k}, k = 0, 1, . . . , n? This is an example of a statistical method used to estimate p when a binomial (n, p) random variable is observed to equal k. If we assume that n is known, then we estimate p by choosing that value of p which maximizes P{X = k}. This is known as the method of maximum likelihood estimation.

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