i have two random variables x e y independent and they're uniform on the interval [0, 1] find cumulative distribution function of Z= (x+y)/(x-y)

i just try to solve...

http://img202.imageshack.us/img202/5647/97250438.jpg

is it right?

Printable View

- Dec 4th 2010, 04:48 PMulissesscumulative distribution function
i have two random variables x e y independent and they're uniform on the interval [0, 1] find cumulative distribution function of Z= (x+y)/(x-y)

i just try to solve...

http://img202.imageshack.us/img202/5647/97250438.jpg

is it right? - Dec 4th 2010, 08:24 PMmatheagle
Z seems to range from -infinity to infinity, this doesn't look good.

AS z approaches infinity this goes to -1/2.

I was playing around with a change of variables with W=X-Y

The joint density of Z and W would be w/2, but the region is 0<w(z+1)<2 and 0<w(z-1)<2 - Dec 5th 2010, 05:30 AMulissess
why the range is [-oo; +oo]? the variables are uniform in [0,1]... i just try the change of variables

http://img338.imageshack.us/img338/4998/34928228.jpg

http://img89.imageshack.us/img89/2320/93533692.jpg - Dec 6th 2010, 01:33 PMulissess
what's the range of this function??