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Integration to d density function

  1. Apr 15, 2005 #1
    I have a problem with an integration, namely:

    Int(from 0 to x) (1-F(x-t)) dF(x)

    and do not know how to calculate....:-(
     
  2. jcsd
  3. Apr 15, 2005 #2

    matt grime

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    If it help,s dF(x) = (dF/dx)dx
     
  4. Apr 15, 2005 #3
    It helps, but that mean to multiply the integrand by the density f=dF/dx and then integrate over dx, so like how to derive the expectation....

    but another problem is, that I do not know the density and need to have a result within F(x)
     
  5. Apr 15, 2005 #4

    matt grime

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    Well, you can do it, though you do'nt think you can. so let#'s play a littel game.

    What's the integral of 1 with respect to x? 1 wrt y? 1 wrt F(x)?

    Now what's the integral of x wrt x? y wrt y, F(s) wrt F(s)?

    Note, I don't think you want an x in the integrand and in the limit.
     
  6. Apr 16, 2005 #5
    That's almost all clear but in my book i read that F(s) wrt F(s) is something like F(s)*F(s) which stands here for the convolution....
    And i have a x in the itegrand as well as in the limit.
    As I said before: int(0 to x) 1-F(x-t) wrt F(t), sorry so you are write, it is F(t) not F(x)!
     
  7. Apr 17, 2005 #6
    Thank you very much for your support, but yesterday i found the answer in my stochastic I scriptum....if someone is interested in:

    Let x, y be independent rvs with dfs F and G then holds for the distribuntion of the sum x+y:

    H(a)=P(x+y<=a)=int F(a-v)dG(v).
     
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