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Let Y denote a Poisson random variable with mean ?. Find
Chapter 3, Problem 165E(choose chapter or problem)
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
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=
Hence the the moment generating function is