A system consists of two components, S1 and S2, ran in series. There is also a replacement part S3 which can instantaneously replace either S1 or S2 if needed. The failure times of all three components are independent and follow exp(1) distributions.

a) Give the expected failure time of the system.

b) Give the distribution (i.e. the cdf) of the failure time of the system. Simplifying your answer is not required.

c) Write a code or detailed psuedocode which simulates the failure time of the system using a software of your choice.

d) Give the expected failure time of the system if S3 had a exp(2) distribution. Simplifying your answer is not required.