Solving Poisson Distributions for Expected Values of Sales

[Hodgey8806]

Homework Statement

A store selling newspapers orders n = 4 of a certain newspaper because the manager does not get many calls for that publication. If the number of requests per day follows a Poisson distribution with mean 3, what is the expected value of the number sold?

Homework Equations

Now we are approximating this with a Poisson distribution as said. So I would think to use 3 because our book explicitly states mean (mu) = sigma^2 = lambda.

The Attempt at a Solution

Thus, my thought is that lamba should be 3 which, I thought should be the expected value. However, I also know through moment-generating functions that the sum of x*P(X=x) is also my expected value. But if I use a lambda of 3, I still can't get the books answer of 2.681.

Thanks for your help!

 

[lippyka]

A:The expected value of a Poisson distribution is the same as its mean, $\lambda$. In your case, $\lambda = 3$. So the expected value is 3.