Let Y have a Poisson distribution with mean ?. Find E[Y (Y

Chapter 3, Problem 138E

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QUESTION:

Problem 138E

Let Y have a Poisson distribution with mean λ. Find E[Y (Y − 1)] and then use this to show that V (Y ) = λ.

Questions & Answers

QUESTION:

Problem 138E

Let Y have a Poisson distribution with mean λ. Find E[Y (Y − 1)] and then use this to show that V (Y ) = λ.

ANSWER:

Solution:

Step 1 of 3:

It is given that Y is a Poisson random variable with mean . Then

P(Y=y)=

We have to find the value of E(Y(Y-1)) and then we have to show that V(Y)=.


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