Revision of probability and stochastic processes
Carlos A. Braumann · 2019
This chapter intends to refresh the basic probabilistic concepts and present the more advanced concepts in probability that are required, as well as to provide a very brief introduction to basic concepts in stochastic processes. In most applications, we will work with random variables that are either discrete or absolutely continuous, although there are random variables that do not fall into either category. In some situations people may not be able to obtain explicit expressions for certain probabilities and mathematical expectations of random variables of interest to them. Instead of giving up, they can recur to Monte Carlo simulations, in which they perform, on the computer, simulations of the real experiment and use the results to approximate the quantities they are interested in studying. The chapter also deals with a more theoretical solid ground approach of conditional probability, conditional expectation, and independence.