Let Y denote a Poisson random variable with mean ?. Find

Chapter 3, Problem 165E

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QUESTION:

Problem 165E

Let Y denote a Poisson random variable with mean λ. Find the probability-generating function for Y and use it to find E(Y ) and V (Y ).

Questions & Answers

QUESTION:

Problem 165E

Let Y denote a Poisson random variable with mean λ. Find the probability-generating function for Y and use it to find E(Y ) and V (Y ).

ANSWER:

Solution

Step 1of 2

We have to find the probability generating function of Y and also we have to find mean and variance of Y

Let Y is the poisson random variable with mean

The pmf of poisson distribution is

The probability generating function of poisson distribution is

                   

                      =

                     

                      =

                   

                      =

                   

                      =

                   

                      =

Hence the the moment generating function is


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