Hello. I have a question about Exercise 5.23 in Jeffrey W. Herrmann's "Engineering Decision Making and Risk Management," 2015. It is a question about the reliability of a system of systems, showing three equations for each of the systems and a sum of the system of systems. The question references the reliability of each system has a beta distribution with different alpha and beta values. This is the first reference to beta distributions and it has not been part of the course. How do I set up this problem? It says to use Monte Carlo sampling to generate 5,000 samples for the system of systems. Can this be calculated by hand or is Excel or MatLab required?

The question ultimately asks for what type of distribution do sample values for the system of systems form and what is the estimated likelihood that the reliability for the system of systems will be at least 0.98.