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(Solved): PLEASE CALCULATE THIS E(Var(YX))+Var(E(YX)) \[ (X, Y) \curvearrowright f(x, y)=\left\{\begin{a ...



PLEASE CALCULATE THIS E(Var(Y?X))+Var(E(Y?X))
\[
(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 \text {
\[ (X, Y) \curvearrowright f(x, y)=\left\{\begin{array}{c} \frac{1}{21}(x+y), \text { for } x=1,2,3 y=1,2 \\ 0, \quad \text { o. w. } \end{array}\right. \] Calculate \( \operatorname{Var}(Y \mid X=1) \operatorname{Var}(Y \mid X=2) \) and \( \operatorname{Var}(Y \mid X=3) \) ?


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Here f(y?x)=f(x,y)f(x) and E(Y?X)=?yyf(y?x)=?yy Now, the marginal distribution of X is f(x)=?yf(x,y) So, f(x=1)=?y=12f(1,y)=f(1,1)+f(1,2) =121(2+3)=52
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