Average of $(1+X)^{-1}$

Question

$X$ has the Poisson distribution with parameter $λ$.

I want to find the average of $(1+X)^{-1}$

Some steps-of-thought would be appreciated.

Do you mean you want to find the expectation of the random variable $Y=\frac{1}{1+X}$? — Alex, Jan 18 '14 at 15:13
2 upvotes for a question with no attempts, kidding me right? — Lost1, Jan 18 '14 at 15:42

score 1 · Accepted Answer · edited Apr 13 '17 at 12:21

1

Here is the same type of question I asked here.

Hint: You need to write $E(1 + X)^{-1}$ in series. Then, evaluate. There is no tricky algebra involved.

edited Apr 13 '17 at 12:21

Community

answered Jan 18 '14 at 15:56

NasuSama

1 Answers1