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 µ1, Y has a Poisson distribution with parameter µ2, 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).
Now sum the joint pmf over (x, y) ε A and use the binomial theorem, which says that

for any a, b.

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