Confusion over term “uniformly distributed” in a probability problem
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I'm trying to determine a joint PDF for random variables $X$ and $Y$ in this problem: $(X,Y)$ is uniformly distributed on the subset of $mathbb R^2$ , defined by $0<X<2$ and $0 <Y<X^3$ . I'm not sure I understand what's meant by "uniformly distributed". Are they saying all valid $(X,Y)$ combinations have equal probability? How does one even begin to define a joint PDF for this? Would it be something like $f_{X,Y}(x,y) = begin{cases}k,&0<X<2, 0 <Y<X^3 \0,& text{otherwise} end{cases}$ Where $k$ is some positive constant
probability probability-distributions
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