Using calculus, it is easier to derive the maximum of the log of the likelihood function, L = log , than the likelihood function  itself. Both functions have a maximum at the same value, so it is sufficient to do either.

a. Calculate the log-likelihood function L(π) for the binomial distribution (1.1).

b. One can usually determine the point at which the maximum of a log-likelihood L occurs by solving the likelihood equation. This is the equation resulting from differentiating L with respect to the parameter and setting the derivative equal to zero. Find the likelihood equation for the binomial distribution and solve it to show that the ML estimate is πˆ = y/n.