An experiment consists of selecting an integer X at random from {1,...,100}and then selecting an integer Y at random from {1,2,....,X}. Calculate E{y} and var Y Solution Again, iterated expectations. E[Y] = E[0.5(1+X)] = 0.5*(1 + E[X]) = 0.5*(1+50.5) = 25.75. Var(Y) = Var(X/12) = 1/144 * Var(X) = 1/144 * (1002)/12 = 10,000/1728..