The document presents a joint probability mass function (pmf) for discrete random variables x and y, defined as pxy(x,y)=(x+2y)/18 for specific values of x and y. It seeks to calculate the conditional mean E[y | x=2]. The joint pmf is valid for x={1,2} and y={1,2}, while being zero for other combinations.

1. Suppose X and Y are discrete random variables which have the joint PMF pXY(x,y)=(x+2y)/18,x=1
,2,y=1,2 and zero elsewhere. Find the conditional mean E[YX=2].