More specifically, if $X$ and $Y$ are independent variables then does $F(X,Y) = F_1(X)F_2(Y)$? Where $F(X,Y)$ is the joint CDF of $X$ and $Y$ and $F_1(X)$ and $F_2(Y)$ are the marginal CDFs of $X$ and $Y$?
2026-03-29 19:11:18.1774811478
What are the properties of the CDF when two variables are independent?
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Yes! $$F(x,y) = P(X \leq x, Y \leq y) = P(X \leq x) P(Y \leq y) = F_X(x) F_Y(y).$$ The second to last equality is where we used the independence of $X$ and $Y$.