Concept explainers
In this exercise, we illustrate the direct use of the Rao–Blackwell theorem. Let Y1, Y2, …, Yn be independent Bernoulli random variables with
That is, P(Yi = 1) = p and P(Yi = 0) = 1 − p. Find the MVUE of p(1 − p), which is a term in the variance of Yi or
a Let
Show that E(T) = p(1 − p).
b Show that
c Show that
and hence that
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Mathematical Statistics with Applications
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