Following from Exercise 40.9, let X be the distribution of the time waited between customers, and let T be the time waited until three customers have arrived. Say whether each of the following statements is true or false, showing any working.

a. T = X1 + X2 + X3 where X1, X2, X3 are independent with the same distribution as X.

b. T = 3X.

c. E(T) = 3E(X).

d. Var(T) = 3Var(X).

e. Var(T) = 9Var(X).