7. Beta and binomial. Let X be a Beta(2, 3) random variable and let Y be a random variable such that Y|X = a: is Binomial(n, x) where n 2 1 is a positive integer. (a) (6 pts) Find the distribution of Y, i.e. compute P(Y=k) for alike {0,...,n}. Hint: For nonnegati've integers a. and b, 1 a b _I'(a.+1)I'(b+1) f0$(1_$)dx_ I'(a.+b+2) ' (b) (4 pts) What is ]E(Y)? Hint: It's not wise to compute it with the weighted sum fonnnta. and (a)