# Expected Value of reciprocal (Sorry for reposting)

by giglamesh
Tags: expected, reciprocal, reposting
 P: 14 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
 Sci Advisor P: 6,027 You need the distribution function for X (the mean is not enough) to get the mean of 1/(X+1).
 P: 14 thanks apparently I do
 P: 523 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).
 Quote by giglamesh There is event Y when calculated it gives the value: $P(Y)=E[\frac{1}{X+1}]$