If X and Y are uniform independent random variables, X~(0,30) and Y~(40,50). I want to know how to find the joint PDF.?
I tried doing it on a rectangle, but i get stuck with the entries. Can u suggest how to proceed?
2026-04-03 04:03:18.1775188998
Joint PDF of Uniform Independent events
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Hint: If two random variables $X$ and $Y$ are independent then
$$f_X(x)\cdot f_Y(y)=f_{X,Y}(x,y) \quad \forall \ x,y \in \mathbb R$$
$f_X(x)$ is the pdf of $X$. Similar for $f_Y(y)$. And $f_{X,Y}(x,y)$ is the joint probability distribution function of $X$ and $Y$.