A pair of random variable $(X, Y)$ is uniformly distributed in the quadrilateral region with $(0,0),(a,0),(a,b),(2a,b)$, where $a,b$ are positive real numbers.
What is the joint pdf $f(X,Y.)$
Find the marginal probability density functions $f_X (x)$ and $f_Y (y)$.
Find $E(X)$and $E(Y)$.
Find $E(X,Y)$.
My understanding is the uniformly distributed pdf $=\frac1{\text{area}}=\frac1{ab}$. It seems that $X$ and $Y$ are independent R.V. because it seems the joint pdf can be factored as $\frac1a \frac1b$ if the pdf is correct. However, after I found the marginal pdf $f_X=\frac2{a^2}; f_Y=\frac2{b}-\frac{2}{b^2}$, which shows $X, Y$ are not independent. If I can not get correct marginal pdf, I can not finish the question d and e. Could anyone help me out? Thank you!