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**1. Given f(x,y) = 2, 0<x<y<1, show V(Y) = E(V(Y|X)) + V(E(Y|x))**

## Homework Equations

I've found [tex]V(Y|X) = \frac{(1-x)^2}{12}[/tex] and [tex]E(Y|X) = \frac{x+1}{2}[/tex]

## The Attempt at a Solution

So, [tex]E(V(Y|X))=E(\frac{(1-x)^2}{12}) = \int_0^y \frac{(1-x)^2}{12}f(x)dx[/tex], correct?