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Math Help - Convolution(sum) of X1~U(0,1) and X2~exp(2)

  1. #1
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    Convolution(sum) of X1~U(0,1) and X2~exp(2)

    where x1 (uniform 0 1) is 0 (t<0), 1 (0<=t<=1), 0 (t>1)
    and x2 (exponential with lambda 2) is 0 (t<0), 2e^(-2t) (t>=0)
    I understand how convolution works, but this problem escapes me.

    I've tried several way using the uniform or the exponential as fx(t-tau), but have had no luck evaluating the integral.

    If somone could show me the correct setup and limits of integration, I would appreciate it.
    Last edited by SlrkcRick51586; April 7th 2010 at 11:11 AM.
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  2. #2
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    \displaystyle\int^t_0 f_{x2}(\tau)*f_{x1}(t-\tau)\,d\tau
    \displaystyle\int^1_{t-1} f_{x2}(\tau)*f_{x1}(t-\tau)\,d\tau
    0 everywhere else?
    yes no maybe?
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