Renewal Age Process. Let Xn denote the renewal age process in Example 20, where the renewals times are i.i.d. machine lifetimes with distribution F and mean μ, and F(1) > F(0) = 0. Prove that Xn is...

Renewal Age Process. Let
_Xn
denote the renewal age process in Example 20, where the renewals times are i.i.d. machine lifetimes with distribution F and mean μ, and F(1) > F(0) = 0. Prove that
_Xn
is ergodic and that its stationary distribution is πi = [1 − F(i)]/μ. Suppose there is a cost C each time the machine is replaced and a cost hi for each period in which the age is i. Give an expression for the average cost for the chainExample 20