4. Coin with random bias (10 points). Consider a coin with random bias P ~ fp(p), i.e., we do not know the bias, but we have a prior on it. Flip the coin and let X = 1 if the outcome is heads and X = 0 if the outcome is tails. Given that X = 1 (i.e., outcome is heads), find fpix (p|1), the a posteriori pdf of P. Let P ~ Unif [0, 1]. Compute the a posteriori pdf of P