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October 30th, 2017, 01:44 PM  #1 
Senior Member Joined: Oct 2015 From: Antarctica Posts: 103 Thanks: 0  Find Joint PDF of two Random Variables
Suppose I know the distributions of two continuous random variables X and Y. Suppose the probability density functions are f(x) and f(y), respectively. Suppose it is known that X and Y are NOT independent. What is the process for finding the joint pdf, f(x, y)? Is there such a general process? Or must more information be known?

October 30th, 2017, 03:33 PM  #2 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,602 Thanks: 816 
You need a conditional distribution or at least a parameter that lets you construct it, or a problem description that lets you derive it. For two normal variates that parameter is the correlation coefficient. 
October 30th, 2017, 06:31 PM  #3 
Senior Member Joined: Oct 2015 From: Antarctica Posts: 103 Thanks: 0 
So suppose they WERE independent. Would the joint pdf simply the the product of their respective pdfs?

October 30th, 2017, 07:06 PM  #4 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,602 Thanks: 816  

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