An Introduction to Probability and Random Variables

Abstract

This chapter is a summary of some key concepts related to probability theory and random variables, with a view to the developments in subsequent chapters. Essential concepts include the formalisation of the intuitive concept of probability, the related concepts of the sample space, the probability space and random variable, and the development of these to cases such as uncountable sample spaces, which are critical to stochastic processes. The reader is likely to have some familiarity with the basic concepts in this chapter, perhaps in the context of countably discrete random variables and distributions such as the binomial distribution and for continuous random variables that are normally distributed.