How to Derive the Joint PDF Using the Ratio of Uniforms Method?

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Discussion Overview

The discussion revolves around deriving the joint probability density function (PDF) using the ratio of uniforms method, specifically in the context of a problem presented in a probability book and a paper from 1977 by Kinderman and Monahan. The focus is on the mathematical process involved in calculating the joint PDF of two random variables, X and Y.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant describes their approach by defining new variables u = y and v = xy, and calculating the Jacobian, which they state is |-y| = y.
  • The same participant expresses difficulty in normalizing the joint PDF using a double integral and requests assistance in obtaining the joint PDF of X and Y.
  • Another participant questions whether the inquiry is related to homework.
  • The initial poster clarifies that the question is from a book and not a homework problem, indicating they are seeking help with a specific mathematical challenge.
  • A later reply from the initial poster states they have found the answer, implying resolution of their query without further elaboration.

Areas of Agreement / Disagreement

The discussion includes a mix of inquiry and clarification, with no explicit consensus reached among participants regarding the method or solution, as the initial poster later claims to have resolved their issue independently.

crazy2006
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Hi everybody:
I am trying to solve this question:
[URL=http://imageshugger.com/][PLAIN]http://imageshugger.com/images/wviidazp3mf06ej32.jpg[/URL]

I have made the following:
u=y
v=xy

Calculated the Jacobian, which is |-y|=y
then as I know that is unnormalized I need to normalized first using a double integral as a normalizing factor, the thing is that I am stuck there :cry:
please could you help me to get the joint pdf of X and Y
thanks
 
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Homework?
 
no homework, this question is posted in a book about probability and also it is somewhat explained into the paper of 1977 of Kinderman and Monahan, but as I said I got stucked into the joint pdf and not get the answer
any help would be valuable
 
nevermind I got the answer, thanks anyway
 

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