I have this question:

http://i44.tinypic.com/r0bclk.jpg

I know I need to find E[X1], E[X2] and E[X3] and then fiddle a bit to get the answers, but when I integrate do I just treat the two variables I am not interested in as constants?

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- Dec 15th 2011, 02:09 PMWevans2303Expectation with 3 variables?
I have this question:

http://i44.tinypic.com/r0bclk.jpg

I know I need to find E[X1], E[X2] and E[X3] and then fiddle a bit to get the answers, but when I integrate do I just treat the two variables I am not interested in as constants? - Dec 16th 2011, 01:45 AMchisigmaRe: Expectation with 3 variables?
By definition the expected value of an is...

(1)

http://www.sv-luka.org/ikone/ikone180a.jpg

Marry Christmas from Serbia

- Dec 16th 2011, 01:06 PMMooRe: Expectation with 3 variables?
Hello,

To be more precise on what chisigma wrote above, you'd be looking for the expected value of (in general, capital letters point to random variables, whereas small letters point to variables).

But here, it's much better to calculate the first 2 moments of , then say that since the joint pdf can be written as functions of only x1, x2 or x3, the three variables are independent. And hence this simplifies quite a lot the calculations, especially for the last 2 expectations.

You'd be able to treat the other rv's as constants if you're considering a conditional expectation with respect to some given rv or sigma-algebra. But given the kind of problem you're working on, it's not something you've studied yet, maybe soon :) - Dec 18th 2011, 12:39 AMmatheagleRe: Expectation with 3 variables?
the marginal densities are obvious by inspection.

You need not integrate out the other variables.

Clearly the density of X1 is cX1 where - Dec 19th 2011, 09:09 AMWevans2303Re: Expectation with 3 variables?
Okay understood, thanks guys. :D

- Dec 26th 2011, 08:29 PMlongchampshopRe: Expectation with 3 variables?
IT's useful,thanks

**Longchamp Classic Large** - Jan 5th 2012, 11:41 AMWevans2303Re: Expectation with 3 variables?
Just an update.

I am using chisigmas method for this question as a means of practice..

for the first one E[3X1+5X2+4X3] is there a shorthand alternative other than calculating the first 2 moments? As opposed to integrating:

E[3X1+5X2+4X3] * (X1X2X3)/3

? - Jan 5th 2012, 11:46 AMmatheagleRe: Expectation with 3 variables?
the density of X3 by inspection, no integration, is on (0,1)

that's a beta distribution, the mean is alpha/(apha+beta)=2/3

you can do the same with the other two random variables, even though they aren't beta's

Then - Jan 5th 2012, 12:00 PMWevans2303Re: Expectation with 3 variables?