We are given a biased coin, where the probability of Heads is q . The bias q is itself the realization of a random variable Q which is uniformly distributed on the interval [0,1] . We want to estimate the bias of this coin. We flip it 5 times, and define the (observed) random variable N as the number of Heads in this experiment.

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

For every positive integers n,k ,

- What is the LMS estimate of Q , given N=3 ?