Suppose X and Y are discrete random variables with the following bivariate distribution. f(x,y) Y = 2 Y=9 X=2 0.2 0.1 X=3 0.1 0.1 X-7 0.1 0.4 Find the marginal distribution of Y y f(y) What is the expected value of Y, E[Y]? Find the conditional distribution of Y, conditional on X = 2 y fly |X=2) What is E[YIX=2] ? Find the conditional distribution of Y, conditional on X = 3 1(yIX = 3) What is E[YIX-3]? Find the conditional distribution of Y, conditional on X = 7 flyIX-7) What is E[YIX=7]? Verify the Law of Iterated Expectations Fill in from your answers and other information above: = E(Y) E(YIX-2)*Pr(X-2)+E(YIX-3)*Pr(X-3) + E(YIX-7)*Pr(X=7)