Two different professors have just submitted final exams for duplication. Let X denote the number of typographical errors on the first professor's exam and Y denote the number of such errors on the second exam. Suppose X has a Poisson distribution with parameter m1, Y has a Poisson distribution with parameter u2, and X and Y are independent. a. What is the joint pmf of X and Y? b. What is the probability that at most one error is made on both exams combined? c. Obtain a general expression for the probability that the total number of errors in the two exams is m (where m is a nonnegative integer). [Hint: A= {(x,y): x+y = m} ={(m, 0),(m-1, 1),.(1, m-1), (0,m) Now sum the joint pmf over (x, y) E A and use the binomial theorem, which says that P1 for any a,b]