a Find the MVUE of PX1 1e hint Hint Consider ux1 1 if x11

(a) Find the MVUE of P(X?1) = (?+ 1)e^(??), hint: Hint: Consider u(x1) = 1 if x1?1. Compute E(U(X1))/Y Where Y=X1+ +Xn (b) Find the asymptotic distribution of the MLE of ? and of P(X?1). (c) Find the asymptotic distribution of the MVUE of P(X??).

Solution

A more friendly way of describing the distribution PD(?) is through the following size-biased sampling process. We first let Uk, k = 1, 2, . . . , be a sequence of independent, identically distributed random variables with common distribution Beta(1, ?). We then generate a random probability vector representing allelic frequencies as follows: X1 = U1, Xn = (1 ? U1)