# Two different professors have just submitted final exams for duplication. Let X denote the number of typographical

## Question:

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 p, Y has a Poisson distribution with parameter , 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), (m1, 1), (1, m-1), (0, m)}. Now sum the joint pmf over (x, y) E A and use the binomial theorem, which says that for any

**a,** b.] m 1-0 m (ab abm-k = = (a + by

## Step by Step Answer:

**Related Book For**

## Probability And Statistics For Engineering And The Sciences

**ISBN:** 9781133169345

8th Edition

**Authors:** Jay L Devore, Roger Ellsbury