Solutions - 5190-03

(1) Compute $P_X(x)$ by summing over $y$:

$$\begin{array}{c}{P}_X(x)=\sum _y{P}_{X,Y}(x,y)\\ \\ \gg \gg P_{X,Y}(x,1)+P_{X,Y}(x,2)\gg \gg \frac{x}{30}(1^2+2^2)\gg \gg \frac{x}{6}\end{array}$$

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(2) Compute $P_Y(y)$ by summing over $x$:

$$\begin{array}{c}{P}_Y(y)=\sum _x{P}_{X,Y}(x,y)\\ \\ \gg \gg \frac{y^2}{30}(1+2+3)\gg \gg \frac{y^2}{5}\end{array}$$