Problem 5.52 A critical component of a system needs to function continuously without failure for 5 days. The distribution of the component’s lifetime is exponential with expected lifetime E(T )=2.5. As soon as he component fails it is immediately replaced by a spare component with the same lifetime distribution. Suppose the system begins with n compo[1]nents, including n − 1 spares. Find the probability that the system functions continuously for the five day period for:

(a) n = 3;

(b) n = 4;

(c) n = 5.