5-54. Suppose that X1, . . . ,Xn are independent continuous random variables, where the probability density function of each Xi appears as f i(x) = -1

λ e−xi /λ, xi > 0, λ > 0, i = 1, . . . , n;

0 elsewhere.

For U = ni

=1 Xi, verify that the moment-generating function for U has the form mU(t) = (1 − λt)−n, t < λ

−1.