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What is the PDF of z where z = x-y

  1. Dec 16, 2013 #1

    I 'm trying to express the PDF of z (z ≥ 0) where z = x-y (and let x,y ≥ 0)

    Thank you in advance
  2. jcsd
  3. Dec 16, 2013 #2


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    Try the above. You should Google "sum of independent random variables".

    For your question you need two things, x and y independent, and let w = -y so you can use standard sum formula for x+w.
  4. Dec 18, 2013 #3
    Thank you for your answer.

    I 'm trying to express the distribution of x-y in integral form. I m not sure about the integration bounds though.

    I presume that the standard convolution PDF can be used: let z= x-y, then:
    fz(z) =∫ fx(x)*fy(z+x) dx, but with what integration lower and upper bounds ??

    Assume that x,y ≥ 0.

    Any help would be useful
  5. Dec 18, 2013 #4


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    The integral is over the whole real line. Since the random variables are assumed non-negative, the integration need only be for non-negative x.
  6. Dec 18, 2013 #5
  7. Dec 19, 2013 #6


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    I am confused about your notation. You seem to have switched x and y between the posts, so I am not sure how you are defining z.

    As far as the upper limit is concerned, infinity is always correct. However because the random variables are non-negative, one of the f's may be 0 past some point, so the integral doesn't need to go any further.
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