# How to find P(x1<x2)

#### statgoon13

##### New Member
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
Just doing the integration directly shouldn't be too bad for this problem.

#### statgoon13

##### New Member
Thanks but if I knew what to integrate I wouldn't have posted the question!

#### Dason

##### Ambassador to the humans
Do you know the joint distribution? Can you draw out the region the defines where x1 < x2?

#### statgoon13

##### New Member
@Dason. No I don't know the joint distribution

#### Dason

##### Ambassador to the humans
The joint distribution of independent random variables is just the product of their corresponding pdfs.

#### statgoon13

##### New Member
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
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.