Is there a way of determining the joint probability density function of two random variables? If we have two independent random variables, $X$ and $Y$ that both are uniform on [0,1], then how do one calculate the joint probability density function, knowing that the two PDFs are 1 each? It wouldn't simply be the product of the two PDFs, right?
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$\begingroup$It would simply be the product of the two pdf's.
If $X$ and $Y$ have densities $f_X$ and $f_Y$ respectively then independence of $X$ and $Y$ is exactly the statement that $(X,Y)$ has density $g(x,y)=f_X(x)f_Y(y)$.
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