Let $x$ and $Y$ be jointly distributed with probability density function,

$f_{x,y}(x,y)=\{\begin{array}{cc}10x^{2}y,& 0yx1\\ 0,& \text{o}\text{t}\text{h}\text{e}\text{r}\text{w}\text{i}\text{s}\text{e}& \end{array}$

a$.$ Find the unconditional and conditional mean of $x.$

b$.$ Show that the unconditional mean of $x$ is the expectation of its conditional mean.

c$.$ Determine the linear regression of $Y$ on $x.$