Let x be a discrete random variable with px -1 2p1 - p
Let X be a discrete random variable with P(X = -1) = 2p(1 - p) and P(X = k) = pk(1 - p)3-k, k = 0, 1, 2, 3, where p ∈ (0, 1).
(a) Determine whether there is a UMVUE of p.
(b) Determine whether there is a UMVUE of p(1 - p).
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