There are two Certified Public Accountants in a particular office who prepare tax returns for clients. Suppose that for a particular type of complex form, the number of errors made by the first preparer has a Poisson distribution with mean value, the number of errors made by the second preparer has a Poisson distribution with mean value , and that each CPA prepares the same number of forms of this type. Then if a form of this type is randomly selected, the function p(x; p) = .5 x! x = 0, 1, 2,... x! gives the pmf of X = the number of errors on the selected form.

a. Verify that p(x: ) is in fact a legitimate pmf ( 0 and sums to 1).

b. What is the expected number of errors on the selected form?

c. What is the variance of the number of errors on the selected form?

d. How does the pmf change if the first CPA prepares 60% of all such forms and the second prepares 40%?