QUESTION # $02$ Random variables $x$ and $Y$ have a joint PDF given by

$f(x,y)=\frac{1}{2\sqrt[\phantom{2}]{3}}$exp$(-\frac{x^2+2xy+4y^2}{6})$

a$)$ Find marginal PDF $fx(x)$ and $fy(y).$

b$)$ Find $E[x],E[Y],$Var$(x)$ and Var$(Y)$

c$)$ Find conditional PDF$,fx|Y(x|y)$

d$)$ Find $E[xY].$