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Convolution problem please help ?

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  • Convolution problem please help ?

    Let x1 x2 x3 be an independent and identically distributed x~uniform(0,1)
    let s=x1+x2+x3 find the pdf and cdf of s ??
    please help me

  • #2
    Originally posted by wahibr View Post
    Let x1 x2 x3 be an independent and identically distributed x~uniform(0,1)
    let s=x1+x2+x3 find the pdf and cdf of s ??
    please help me
    f_x1 = f_x2 = f_x3 = 1
    I believe it is a two steps problem.
    1) t = x1+x2
    2) s = t + x3

    1)f_t(t) = Integral from 0 to t [f_x1(x1) * f_x2(t-x1) dx1]=
    = Integral from 0 to t (1 dx1) = t , so f_t(t)=t
    2) f(s) = Integral from 0 to s [ f_t(t)*f_x3(s-t) dt] =
    = Integral from 0 to s [ t dt] = (s^2)/2

    Then F(s) = Integral from 0 to s [ f_s(x) dx] = (s^3)/6.

    Please, someone correct me if I am wrong.

    Comment


    • #3
      Convolution is a very difficult technique and you will be hard pressed to find questions and solutions that use it. ASM has some convolution questions. My advice is to just not use it--transformation questions can be done in a whole variety of ways. Good luck.

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      • #4
        this is not just the matter to pass the exam the concept must be clear buddy
        :smiloe:

        Comment


        • #5
          @ AsyaK

          I think the pdf may be three part function 0<s<1 , 1<s<2 , 2<s<3

          this one is not looking right

          Comment


          • #6
            Originally posted by Talha Malik View Post
            Convolution is a very difficult technique and you will be hard pressed to find questions and solutions that use it. ASM has some convolution questions. My advice is to just not use it--transformation questions can be done in a whole variety of ways. Good luck.
            Studying only the imaginary minimum needed to pass is a common way to fail actuarial exams. You should learn convolution.
            Sincerely,
            Krzys' Ostaszewski
            Want to know how to pass actuarial exams? Go to: smartURL.it/pass

            Comment


            • #7
              Originally posted by AsyaK View Post
              f_x1 = f_x2 = f_x3 = 1
              I believe it is a two steps problem.
              1) t = x1+x2
              2) s = t + x3

              1)f_t(t) = Integral from 0 to t [f_x1(x1) * f_x2(t-x1) dx1]=
              = Integral from 0 to t (1 dx1) = t , so f_t(t)=t
              2) f(s) = Integral from 0 to s [ f_t(t)*f_x3(s-t) dt] =
              = Integral from 0 to s [ t dt] = (s^2)/2

              Then F(s) = Integral from 0 to s [ f_s(x) dx] = (s^3)/6.

              Please, someone correct me if I am wrong.
              You are wrong. The PDF of T is t for 0 < t < 1 and 2 - t for 1 < t < 2. This is done in detail in section 3 of the ASM Manual.

              This is a relevant reference in Wikipedia for this problem: http://en.wikipedia.org/wiki/Irwin–Hall_distribution
              Yours,
              Krzys'
              Last edited by krzysio; May 25 2010, 02:54 AM.
              Want to know how to pass actuarial exams? Go to: smartURL.it/pass

              Comment


              • #8
                Originally posted by krzysio View Post
                You are wrong. The PDF of T is t for 0 < t < 1 and 2 - t for 1 < t < 2. This is done in detail in section 3 of the ASM Manual.

                This is a relevant reference in Wikipedia for this problem: http://en.wikipedia.org/wiki/Irwin–Hall_distribution
                Yours,
                Krzys'
                Thanks!
                Isn't n = 3 for this problem? Is this case (n=3) done in ASM Manual?

                Comment

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