Please answer question 3 (at the end) while ignoring the answers provided. Thank you.

The probability of Heads of a coin is y, and this bias 3; is itself the realization of a random variable Y which is uniformly distributed on the interval [0,1]. To estimate the bias of this coin. We flip it 6 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 to, k, talk! 1 n k _ f0": (1\"?) dx' (n+k+1)1' 1. Given the observation N = 3, calculate the posterior distribution of the bias Y. That is, find the conditional distribution of Y, given N=3. ForlgyglI 140-y3-(1-yla 2. What is the LMS estimate of Y, given N = 3? (Enter an exact expression or a decimal accurate to at least 2 decimal places.) in\": 3. What is the resulting conditional mean squared error of the LMS estimator, given N = 3? (Enter an exact expression or a decimal accurate to at least 2 decimal places.) 1/36