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Let 'X' and 'Y' be two dependent continuous random variables whose marginal PDFs ($f_X(x)$ and $f_Y(y)$) are known. Then, how can we find their joint PDF i.e., $f_{XY}(x,y)$ . Is there any method to calculate this ?

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    $\begingroup$ No. You cannot do this without further information. $\endgroup$ Jul 3, 2022 at 6:42

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No, there is not. If the two random variables were independent then their joint PDF would be $f_{XY}(x,y)=f_X(x)f_Y(y)$.

In in the case of dependent random variables we cannot infer anything, not even that the joint distribution is continous. For instance, let $X$ be a random variable following Uniform Continous Distribution on $[0,1]$ and let's define $Y=1-X$. Then, it can be proven that $X$ and $Y$ are not jointly continous.

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