Let $X$ and $Y$ be continuous random variables with joint PDF $f(x,y) = kxy^2$ and support set $0
a) Find the constant $k$. $k = 60$? This is what I got.
b) Find the marginal PDFs of $X$ and $Y$. (I know for $X$ you take the integral from $0$ to $\infty$ of $f(x,y) dy$ and vice versa for $Y$.)
c) Find $\mathbf E(X|Y = y)$ and $\mathbf E(Y|X =x)$.
d) Find the correlation coefficient, which is $\frac{\mathbf E(XY) - \mathbf E(X) \mathbf E(Y)}{\sqrt{\mathbf E(X^2)-\mathbf E(X)}\sqrt{\mathbf E(Y^2)-\mathbf E(Y)}}$.
e) Find $\mathbf P(Y<4X/5+2/3)$
I know how to do most of this but I don't know how to find the constant $k$? I got $k = 60 $ but I'm not sure its correct? Help? Thank you in advance.