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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 [itex]\bar{X}[/itex]

There is event Y when calculated it gives the value:

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

The QUESTION: Is there a way to find expected value [itex]\bar{Y}[/itex] in the terms of [itex]\bar{X}[/itex]? 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):

[itex] E[\frac{1}{X+1}]=\frac{1}{E[X]+1}[/itex]

Thanks and sorry for repost

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 [itex]\bar{X}[/itex]

There is event Y when calculated it gives the value:

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

The QUESTION: Is there a way to find expected value [itex]\bar{Y}[/itex] in the terms of [itex]\bar{X}[/itex]? 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):

[itex] E[\frac{1}{X+1}]=\frac{1}{E[X]+1}[/itex]

Thanks and sorry for repost

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