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Conditional CDF query

  1. Apr 3, 2014 #1
    Hello.

    I was wondering if the following is correct.

    Let S= a*X/(b*X+c), where a,b,c are positive constants and X is a positive random variable. Also let H= h, where h is also a positive random variable (S and H are mutually independent).

    Then, let F_{Z}(.) and f_{Z}(.) denote the CDF and PDF of Z, respectively. Thus, does the following holds true?

    F_{S}(y) = ∫ F_{S|H}(a*X/(b*X+c) <= y | H) * f_{H}(h) dh.

    Thank you in advance.
     
  2. jcsd
  3. Apr 3, 2014 #2

    mathman

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    Science Advisor
    Gold Member

    You say H and S are independent. In that case F_{S|H} = F{S}. Therefore the expression hold trivially.
     
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