Problem 4E

Generalize Exercise 5.4-3 by showing that the sum of n independent Poisson random variables with respective means μ1,μ2, . . . ,μn is Poisson with mean

References Exercise 5.4-3

Let X1, X2, X3 be mutually independent random variables with Poisson distributions having means 2, 1, and 4, respectively.

(a) Find the mgf of the sum Y = X1 + X2 + X3.

(b) How is Y distributed?

(c) Compute P(3 ≤ Y ≤ 9).

Problem 4E

Generalize exercise 5.4.3 by showing that the sum of n independent Poisson random variables with respective means is Poisson with mean

Step by Step Solution

Step 1 of 2

The MGF of Poisson distribution with parameter is

Letbe mutually independent random variables with Poisson distribution having means respectively.

Then, the MGF of is