E3 Suppose that B1 Bn Bernoullip with p unknown Joe wants

E3 Suppose that B1,.. . , Bn Bernoulli(p), with p unknown. Joe wants to estimate p via hat Pjoe - beta1. Julie complains that hat pjoej ignores most of the data, and proposes to use the Rao-Blackwellized version of hat pjoe instead. What is Julie?s estimator?

Solution

An estimator ?(X) is an observable random variable (i.e. a statistic) used for estimating some unobservable quantity. For example, one may be unable to observe the average height of all male students at the University of X, but one may observe the heights of a random sample of 40 of them. The average height of those 40