11.6 Denote by L(t) = XN(t)+1 the random variable measuring the current lifetime at t. Suppose the renewal process has discrete lifetimes. Let n ≥ 1, and set z(n) = P(Lt = n). Show that z(n) satisfies the renewal equation (11.5) with bn =



f(t), for n = 0, 1, 2,...,t − 1 0, for n ≥ t

.