In order to increase the lifetime of the system, the engineers have a choice between replacing component A with one whose lifetime is distributed Exp(1/2), or replacing component B with one whose lifetime is distributed Exp(1/3).

a. Generate, by simulation, a large number (at least 1000) of system lifetimes under the assumption that component A is replaced.

b. Generate, by simulation, a large number (at least 1000) of system lifetimes under the assumption that component B is replaced.

c. If the goal is to maximize the mean system lifetime, which is the better choice? Explain.

d. If the goal is to minimize the probability that the system fails within a month, which is the better choice? Explain.

e. If the goal is to maximize the 10th percentile of the system lifetimes, which is the better choice? Explain.