Let Y1, Y2, . . . , Yn be independent and identically distributed random variables such that for

0 < p < 1, P(Yi = 1) = p and P(Yi = 0) = 1 p.

(a) Find a sufficient statistic for p.

(b) Find the ML estimator

p of p.

(c) Find the ML estimator

of = p(1 p).

(d) Give a MVUE for p.