Pregunta: (X,Y)↷f(x,y)={211(x+y), for x=1,2,3y=1,20,o.w. VerifyVar(Y)=E(Var(Y∣X))+Var(E(Y∣X))

First we will need to find the conditional distribution Y|X

$\mathrm{P}(\mathrm{Y}=\mathrm{y}\mid \mathrm{X}=\mathrm{x})=\frac{\mathrm{P}(\mathrm{Y}=\mathrm{y},\mathrm{X}=\mathrm{x})}{\mathrm{P}(\mathrm{X}=\mathrm{x})}$ (*)

So we see that we need the marginal d...