Chapter 4 Conditional Expectation and the BLP

Let us roll two dice, and define random variables \(X\) and \(Y\) as the difference and sum of the face-values, respectively. Depending on what nature decides to choose when the dice are rolled, the random variable \(X\) can output a number from \(\{-5,-2,-1,0,1,2,3,4,5\}\) and \(Y\) a number from \(\{2,3,\ldots,12\}\).

If \(X=5\), then the face-values are \((6,1)\)f