3. Suppose we have a coin that has a 0 probability of Heads. We don't know the parameter 0, but we assume its prior distribution is 0 ~ Uniform {0.25, 0.5, 0.75} (this is a discrete uniform distribution, placing equal probability on each value in the finite list). The data we observe is X, the outcome of a single flip of the coin, with X = 1 for Heads and X = 0 for Tails. (a) Write down a hierarchical model for the data X. (b) Compute P(X = 1). (c) What is the posterior distribution of the parameter 0 (i.e., the conditional distribution of 0 | X)? (d) Suppose we observe X = 1. Now we will flip the same coin again, to obtain a new outcome Y. Conditional on what we've observed so far, what is the probability that Y = 1