The joint density of $X$ and $Y$ is given by
$$ f(x,y) = \left\{ \begin{array}{l l} 1/2 & \quad \text{$|x|+|y|\leq 1$}\\ 0 & \quad \text{otherwise} \end{array} \right.$$
Show that $Y$ has constant regression with respect to $X$ and/but that $X$ and $Y$ are not independent.
So far I have that the marginal density function for $X$ is $$f_{X}(x)=\int_0^{1-x}\frac{1}{2}dy=\frac{1-x}{2} \quad \text{for $0<x<1$}$$ and the marginal density function for $Y$ is $$f_{Y}(y)=\int_0^{1-y}\frac{1}{2}dx=\frac{1-y}{2} \quad \text{for $0<y<1$}.$$ Also, $$\mathbb{E}(Y|X=x)=\int_0^{1-x}y(1-x)dy=-\frac{1}{2}(x-1)^3 (=\mathbb{E}Y?).$$ I don't exactly know what I'm trying to show. Does anyone know where to go from here?