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Math Help - Random Variable Distribution

  1. #1
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    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.
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  2. #2
    Moo
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    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
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