Question: With a beta prior for the binomial parameter ???? having ???? = ????1(????1 + ????2) and letting n = ????1 + ????2, find E( ????

With a beta prior for the binomial parameter ???? having ???? = ????1∕(????1 + ????2)

and letting n∗ = ????1 + ????2, find E( ̃???? − ????)

2 and express it as a weighted average of [????(1 − ????)]∕n and (???? − ????)

2. Compare this with E( ̂???? − ????)

2, for ̂???? = y.

Evaluate when the Bayes estimator is better and when the ML estimator is better.

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