# Thread: How to integrate a Function of Random Variables using joint probability density?

2. ## Re: How to integrate a Function of Random Variables using joint probability density?

integration by parts will take care of this easily enough

3. ## Re: How to integrate a Function of Random Variables using joint probability density?

@romsek yes that what I was thinking yet the answer the book gets is very baffling indeed.

I am sorry to trouble you with my trifles but would it be possible if you could show me what is u and what is dv?

4. ## Re: How to integrate a Function of Random Variables using joint probability density?

Originally Posted by littlejon
@romsek yes that what I was thinking yet the answer the book gets is very baffling indeed.

I am sorry to trouble you with my trifles but would it be possible if you could show me what is u and what is dv?
$\displaystyle{\int_0^\infty}~u e^{-u}~du$

let's rewrite this in $x$ to avoid confusion

$\displaystyle{\int_0^\infty}~x e^{-x}~dx$

$u=x,~du=dx$

$dv = e^{-x}~dx,~v = -e^{-x}$

$\left . -x e^{-x}\right |_0^\infty + \displaystyle{\int_0^\infty}~e^{-x}~dx=$

$\displaystyle{\int_0^\infty}~e^{-x}~dx=1$

5. ## Re: How to integrate a Function of Random Variables using joint probability density?

Originally Posted by romsek
$\displaystyle{\int_0^\infty}~u e^{-u}~du$

let's rewrite this in $x$ to avoid confusion

$\displaystyle{\int_0^\infty}~x e^{-x}~dx$

$u=x,~du=dx$

$dv = e^{-x}~dx,~v = -e^{-x}$

$\left . -x e^{-x}\right |_0^\infty + \displaystyle{\int_0^\infty}~e^{-x}~dx=$

$\displaystyle{\int_0^\infty}~e^{-x}~dx=1$

What does the Gamma mean?

6. ## Re: How to integrate a Function of Random Variables using joint probability density?

Originally Posted by littlejon
What does the Gamma mean?
wat?

I don't see any Gamma anywhere

7. ## Re: How to integrate a Function of Random Variables using joint probability density?

Sorry for the late reply in the book the answer was 2Γ =1. I was wondering where the gamma came from. I guess it is not so important if you can solve it without it.