If X and Y are correlated exponential Random variables and they are no longer independent(they are Correlated now) how can I find joint PDF of X and Y ? If they are independent I have to just multiply their PDFs to get joint PDF but now what to do?
2026-03-27 08:56:36.1774601796
Joint PDF (probability density functions) of two correlated (non-independent) random varaiables
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You can't in general know the joint PDF from the marginals. That loss of information is fundamentally what makes them correlated. Formally, we can see this by noticing:
$$ P(A, B) = P(A|B) P(B) \neq P(A)P(B) $$
So we need the quantity $P(A|B)$, but if all we have is $P(A)$ we're out of luck.