A random point x$=($x$,$Y$)$ ?is drawn uniformly from the triangle in the xy plane depicted below.

$($a$)$ ?Determine the values E$($X$)$ ?and E$($XY $).($Lead: Show that the conditional expectation E$($X$|$Y $)=0$ ?for all Y in $[0,2].)$

$\mathrm{ (}$b$)$ ?Determine the variance matrix K $=$ ?V$($X$)$ ?of the vector X $=($X$,$ ?Y $)$

-1 2 Y (X,Y) 1 X