2. Beta-Bernoulli practice (a) Assume y; ~ i.i.d Bernoulli(9). Write out the likelihood for 9 given observations 91, ...yn. Simplify by removing proportionality constants. (b) Assume the prior 10(3) ~ Beta(a, b). What is the posterior distribution for 9? (c) How do we interpret a and b in terms of pseudo-counts? ((1) Find the posterior mean. Write it in terms of a weighted average of the MLE and the prior mean