## Expected Value of reciprocal (Sorry for reposting)

Hi all
Sorry for reposting, the previous post wasn't clear enough, it's my mistake, I'll make the question more clear, I found lot of people asking the same question on the Internet.

Given that X is random variable that takes values:

0..............H-1

The PMF of X is unknown, but I can tell what is the expected value which is $\bar{X}$

There is event Y when calculated it gives the value:

$P(Y)=E[\frac{1}{X+1}]$

The QUESTION: Is there a way to find expected value $\bar{Y}$ in the terms of $\bar{X}$? regarding that: the PMF of X is unknown we know just the expected value.

It's wrong to say that (just if you can confirm it will be great):
$E[\frac{1}{X+1}]=\frac{1}{E[X]+1}$
Thanks and sorry for repost

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 Recognitions: Science Advisor You need the distribution function for X (the mean is not enough) to get the mean of 1/(X+1).
 thanks apparently I do

## Expected Value of reciprocal (Sorry for reposting)

If X is strictly positive, you can apply Jensen's inequality etc. to get 1 >= E[1/(X+1)] >= 1/(E[X]+1).

Recognitions:
 Quote by giglamesh There is event Y when calculated it gives the value: $P(Y)=E[\frac{1}{X+1}]$