Let the random variables $X$ and $Y$ have a joint PDF which is uniform over the triangle with vertices at $(0, 0), (0, 1 )$ and $(1, 0)$.
Find the joint PDF of $X$ and $Y$.
Someone answered
$$S=\{(x,y)\in \Bbb R^2: 0\le x\le 1, \; 0\le y\le 1-x\}$$
my drawing:
Problem 1: I don't know why he represent $y$ as $1-x$, instead of just $0\leq y \leq 1$. To my understanding, $x,y$ can be any point $0\leq x,y \leq 1$. I know the longest side of triangle is $x+y=1$, but dont know what's the relationship.
Problem 2: Also, why someone call it joint PDF, someone call it multivaible PDF, which one is correct?