Question: We are given a biased coin , where the probability of Heads is a . The bias a is itself the realization of a random

We are given a biased coin , where the probability of Heads is a . The bias a is itself the realization of a random variable @ which is uniformly distributed on the interval O , 1 . We want to estimate the bias of this 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 20 t ( 1 - 20 ) " doc It ! ( 12 + 1 + 1 ) ! 1 . Given the observation N - 3 calculate the posterior distribution of the bias @ That is find the conditional distribution of Q . given N = 3 For OS q

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