$f(x, y) = 6x$ for $ 0 \leq x \leq y \leq 1$
How do I calculate the marginal pdfs in this equation? I haven't done double integrals in years and can't understand how this works.
2026-03-25 20:10:56.1774469456
Marginal pdf of Jointly Distributed RVs
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To get the marginal for $x$ you integrate the joint PDF over $y.$ The resriction $0\le x \le y\le 1$ tells you how to do the bounds. So you have $$ f_X(x)= \int_x^1 f_{X,Y}(x,y)dy = \int_x^1 6x dy = 6x(1-x).$$ Note the $6x$ is constant with respect to $y$ to it comes out of the integral.
I'll leave $f_Y(y)$ up to you.