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October 30th, 2017, 01:44 PM   #1
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Question 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?
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October 30th, 2017, 03:33 PM   #2
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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.
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October 30th, 2017, 06:31 PM   #3
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So suppose they WERE independent. Would the joint pdf simply the the product of their respective pdfs?
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October 30th, 2017, 07:06 PM   #4
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Quote:
Originally Posted by John Travolski View Post
So suppose they WERE independent. Would the joint pdf simply the the product of their respective pdfs?
yep
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