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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.

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# Conditional CDF query

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