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 A 5 E(x, y): | x 2 y | # 1 6 F f(x, y) 5 e K(x2 1 y2

)

distribution with parameter m1, Y has a Poisson distribution with parameter m2, 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) A and use the binomial theorem, which says that for any

a, b.]