Imagine that you wish to estimate the fraction of a population that is female. Suppose you take a random sample of n individuals from the population, and k of them are female. Suppose further that the population is large enough relative to n that your sample has a negligible effect on the fraction of females in the remaining population. In this case we can model the number of females in the sample as a binomial random variable with unknown parameter p.(a) What is the probability of obtaining the observed sample as a function of p? 

P(X = k) = nCk *p^k (1 - p)^n - k

The function obtained in part (a) is referred to as a likelihood function. The maximum likelihood estimate for p is the value of p that maximizes the likelihood function. What is the maximum likelihood estimate of the fraction of females in the population p^, where the 'hat' indicates that this value of p is the maximum likelihood estimate?