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## #1 2013-03-07 07:44:55

White_Owl
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### Expected value of a function of a random variable

The problem states:

The weekly demand for propane gas (in 1000s of gallons) from a particular facility is an rv X with pdf

If 1.5 gallons are in stock at the beginning of the week and no new supply is due in during the week, how much of the 1.5 thousand gallons is expected to be left at the end of the week? [hint: let h(x)=amount left when demand =x.]

As far as I understand, to solve the problem I need to calculate:

And E(h(X)) would be the answer for the problem. But what is the h(x)??? Is it (1.5-x) or is it something else?

## #2 2013-03-07 07:58:49

White_Owl
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### Re: Expected value of a function of a random variable

Ok, I tried it both ways and got:

if h(x)=1.5-x, then

if h(x)=x-1.5, then

Maybe I do not understand it at all, but: If pdf is defined for the [1,2] range, does that mean that we expect "the demand" to be at least 1, but no more than 2? but from this point of view the 1.5 at the beginning of the week will satisfy part of the demand and at the end of the week we would have a shortage. So negative amount should be the correct answer?

## #3 2013-03-07 09:18:55

bobbym

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### Re: Expected value of a function of a random variable

You can not have here a minus expectation of oil left. I think you say it is 0.

Last edited by bobbym (2013-03-07 22:10:29)

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
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