In: Statistics and Probability
Let Y1,Y2,...,Yn be a Bernoulli distributed random sample with P(Yi = 1) = p and P(Yi = 0) = 1−p for all i.
(a) Prove that E(¯ Y ) = p and V (¯ Y ) = p(1−p)/n2, for the sample mean ¯ Y of Y1,Y2,...,Yn, and find a sufficient statistic U for p and show it is sufficient for p.
(b) Find MVUE for p and show it is unbiased for p.