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.

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- Nov 4th 2009, 07:46 AMgizmoRandom 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. - Nov 4th 2009, 11:23 AMMoo
Hello,

Make a Jacobian transformation of the pdf, by considering $\displaystyle \varphi ~:~ (x,y) \mapsto (d,y)=(x-y,y)$. 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 :)