We are given a biased coin, where the probability of Heads isq . The biasqis itself the realization of a random variableQwhich is uniformly distributed on the interval[0,1] . We want to estimate the bias of this coin. We flip it5times, and define the (observed) random variableNas the number of Heads in this experiment.

Throughout this problem, you may find the following formula useful:

For every positive integersn,k ,

1. What is the resulting conditional mean squared error of the LMS estimator, givenN=3 ?