Let X have Poisson distribution. Calculate:

a) E(3X+5)
b)Var(3X+5)
c) E(1/(1-x))

Can you assume independence and use the additive/distributive properties? I don't understand which equation I am supposed to be using...
Thank you!!!

Hello,

well, if you want to be complicated... any random variable is independent with any constant.

But for the first question, you just have to use the linearity of the expectation : E(aX+b)=aE(X)+b, where a and b are constants.

For the second question, Var(aX+b)=a²Var(X), because Var(constant)=0, and if you don't see why, go back to the definition of the variance.

For the last question, is it x or X ?

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It's big X

I can calculate E(1/(1+X)), but I have trouble with E(1/(1-X)).
The part where x=1 in the series causes trouble.
It's 3am and I'm tired.
I need to revise one paper, work on an example or two on another and continue with the simulations on a third paper.