An auditor is checking tax returns for fraud. They need to find Y returns with irregularities to review in detail and Y is known to be Poisson with mean 10. The probability that any particular return has an irregularity is 0.05 (independent). Let X=total number of returns the auditor checks a) What is the conditional distribution of X|Y=y? b) Find E(X|Y=y) and Var(X|Y=y) Find E(X|Y) and Var(X|Y) Find E(X) e Find Var(X) For each return that does NOT have an irregularity, the cost in lost productivity has a gamma distribution with a = 3 and 1 = 4. Calculate the mean and variance of the Total Cost