Question

We are given a biased coin , where the probability of heads is q. he 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 the coin. We flip it 5 times, and define the(observed) random variable N as the number of heads in the experiment. Throughout this problem, you may find the following formula useful: x^n(1-x)^kdx= n!k!/(n+k+1)!.
1.Given the observation N=3. Calculate the posterior distribution of the bias Q.
2.What is the LMS estimate of Q, given N=3.
3.What is the resulting conditional mean squared error of the LMS estimator, given N=3.