# Random Variable Distribution

• November 4th 2009, 08:46 AM
gizmo
Random Variable Distribution
I'm stuck on starting this question, any help would be great:

- X and Y are independent identically distributed random variables with exponential distributions of the form,

f(t)=(1/B)exp(-t/B)

If D=X-Y find the distribution of D.
• November 4th 2009, 12:23 PM
Moo
Hello,

Make a Jacobian transformation of the pdf, by considering $\varphi ~:~ (x,y) \mapsto (d,y)=(x-y,y)$. You'll have the pdf of (D,Y).
Then integrate with respect to the second variable to get the marginal pdf of D.

If you still struggle with that, let us know :)