1. - 16 points Given are two jointly continuous random variables $Y_1$, $Y_2$ with joint PDF
$f_{Y_1, Y_2}(y_1, y_2) := egin{cases} rac{e^{-y_1/2 - y_2/3}}{6}, & \text{if } 0 \le y_1, y_2 < \infty, \
0, & \text{else.} \end{cases}$
(a) Compute the marginal distribution $f_{Y_1}(y_1)$.
(b) Compute $f_{Y_2|Y_1}(y_2 | y_1)$.
(c) Compute $E[Y_1]$, $E[Y_2]$, $E[Y_1Y_2]$.
(d) Compute $Var[Y_1 + Y_2]$.