Reference no: EM132857645

-Suppose we have a coin that has a θ probability of Heads. We don't know the parameter θ, but we assume its prior distribution is θ ∼ 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 θ (i.e., the conditional distribution of θ | 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?