Hi! I appreciate your help with the result and approach for these questions. Thanks!

Problem 5 5.0 points possible {graded, results hidden} 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 [{1, 1]. To estimate the bias of this coin. We flip it 3 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, nlk! 1 11 h _ [am (1'3) dz{n+k+1)!' 'i. Given the observation N = 3, calcuiate the posterior distribution of the bias Y. That isr find the conditional distribution of Y, given N = 3. Forilyii 1r fwry I N =3) = 2. What is the LMS estimate of Y. given N = 3? [Enter an exact expression or a decimal accurate to at least 2 decimal pieces.) .t YLMS = 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.) 5 TAN [if-RD HOTAT | UN