Let Y1,Y2,...,Yn be a Bernoulli distributed random sample with P(Yi = 1) = p and P(Yi...

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.

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orchestra answered 2 years ago

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