How to find P(x1<x2)

#1
X2 and x1 being 2 independent exponential variables with mean 5 and 2.
I found f(x1) and f(x2) and defined y as x2 - x1 but I'm stuck there. How do I calculate f(y)? or is there another way of finding P(x1<x2).
Thank you!
 

Dason

Ambassador to the humans
#6
The joint distribution of independent random variables is just the product of their corresponding pdfs.
 
#7
I did not do it with the joint function. I integrated f(x1) from 0 to x2 and subtracted the result from 1.
I was wondering if I should have used y=x1-x2 instead and solve P(y>0)
 

Dason

Ambassador to the humans
#8
I did not do it with the joint function. I integrated f(x1) from 0 to x2 and subtracted the result from 1.
How does that get you the answer? Wouldn't that be a function of x2 still?
I was wondering if I should have used y=x1-x2 instead and solve P(y>0)
That is one way to do it but it isn't nearly as easy as the method I mentioned earlier.