Hello.(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Conditional CDF query

Loading...

Similar Threads - Conditional query | Date |
---|---|

A Value at Risk, Conditional Value at Risk, expected shortfall | Mar 9, 2018 |

I Equality in conditional probability | Jan 18, 2018 |

I Rewriting of equality in conditional probability distribution | Jan 16, 2018 |

B Conditional Probability, Independence, and Dependence | Dec 29, 2017 |

I Dijkstra's algorithm - Shortest Path Query | Jan 8, 2017 |

**Physics Forums - The Fusion of Science and Community**