# Homework Help: Applied Stochastic Processes - 2?

1. Oct 24, 2013

### ra_forever8

Two independent random variables X and Y has the same uniform distributions in the range [-1..1]. Find the distribution function of Z=X-Y, its mean and variance.

=Using change of variables technique seems to be easiest.

fX(x) = 1/2

fY(y) =1/2

f = 1/4 ( -1<X<1 , -1<Y<1)

Using u =x -y , v= x+y

Jacobian is del (x,y) / del (u,v) = 1/2

then J =1/2

and g (u,v) =1/8

Integrate g with respect to v then

gu = (u+2)/4 -2<u<0

and gu = ( -u+2) /4 , 0< u<2

is the PDF of u

Finally mean and variance, Can someone help me? Thanks

2. Oct 24, 2013

### Ray Vickson

You don't need to know g(u) to do these last two questions. However, since you have already obtained g(u), what is stopping you from using it to compute EZ and Var(Z) directly?

Also: please change the title of new posts on similar topics; we try to use titles to keep thing straight, and confusion can result when more than one of post from the same person has the same title. You could even use the same title but with suffixes such as 1,2, etc, or a,b,c,... .

Last edited by a moderator: Oct 24, 2013
3. Oct 24, 2013

### Staff: Mentor

Questions involving integration and Jacobians are more suited to the Calculus & Beyond section. I am moving the thread to that section.