(Solved): \( (X, Y) \curvearrowright f(x, y)=\left\{\begin{array}{c}\frac{1}{21}(x+y), \text { for } x=1,2,3 ...

\( (X, Y) \curvearrowright f(x, y)=\left\{\begin{array}{c}\frac{1}{21}(x+y), \text { for } x=1,2,3 y=1,2 \\ 0, \quad o . w .\end{array}\right. \) \( \operatorname{Verify} \operatorname{Var}(Y)=\mathrm{E}(\operatorname{Var}(\mathrm{Y} \mid X))+\operatorname{Var}(\mathrm{E}(\mathrm{Y} \mid X)) \)