Let X andY be respectively the number of cups of tea and coffee a randomly-chosen classmate of yours drank at breakfast-time today. Assume that none of your classmates would ever drink both tea and coffee at a single breakfast event, but that some of them drink tea and some drink coffee. Say whether each of the following statements is true or false. Briefly explain your answers.

a. E(X+Y) = E(X)+E(Y) even though X andY are dependent.

b. E(XY) = E(X)E(Y) despite the dependence between X and Y.

c. E(XY) = 0 in this example, so it isn’t equal to E(X)E(Y).

d. Var(XY) = 0 in this example.

e. Var(X + Y) = Var(X) + Var(Y) in this example.