Question - Let {X1.... Xn} be random sample from bernoulli distribution with P (X1 = 1) = ∏ = 1 - P(X1 = 0). Let ∏(hat) = X(hat) = (X1 +.. Xn)/n be estimator for ∏.

Find MSE (∏(hat)). Is ∏(hat) unbiased and is it consistent?

Let Y = X1...+ Xn. Find distribution of Y

Find distribution of ∏(hat)

Literally so confused.. I know what MSE is but not how to find it wth the info given. Would appreciate if someone could help me out with understanding this.

Thanks