2.29 Depending on the weather conditions, the probability that an egg hatches is a random variable P distributed according to a Beta distribution with parameters a and

b. A hen deposits 20 eggs and it is reasonable to assume that the total number of eggs that hatch is a random variable X, which has a binomial distribution with parameters 20 and P.

a) Calculate the joint distribution of X and P.

b) Calculate the marginal distribution of X (this distribution is called the betabinomial distribution).