The joint density function $f_{x,Y}(x,y)$ is given by

$f_{x,Y}(x,y)=\{\begin{array}{ccc}\frac{12}{49}(2+x+xy+4y^2),& 0x1,& 0y1\\ 0,& \text{o}\text{t}\text{h}\text{e}\text{r}\text{w}\text{i}\text{s}\text{e}& \end{array}$

a$)$ Compute $f_x(x)$ for all $xin{R}^1.$

b$)$ Compute $f_Y(y)$ for all $yin{R}^1.$

c$)$ Determine whether or not $x$ and $Y$ are independent.