This is a product of three terms. The first term is 0 when = 0. The second is 0 when = 1. The third is zero when = . The solution that maximizes the likelihood is clearly = (since = 0 and = 1 result in a likelihood of 0). Thus the maximum likelihood estimator for is .
this IS A proDuCt of thrEE tErMs. the fIRst teRM is 0 When = 0. the seCond is 0 wHen = 1. the ThirD is zerO wHEn = . tHE SolUtion ThaT maxIMizEs tHe liKelihoOD IS cleArly = (sincE = 0 ANd = 1 reSult IN a lIKELihood of 0). thUS the MaxIMUM likElihooD EsTiMaTOr for Is .