1 - Probability Concepts

Summary

This chapter introduces the probability concepts of experiments, events, distributions, random variables and expectation through Matlab examples. It then outlines set theory and the three actions complement, union and intersection using Venn diagrams. The Kolmogorov axioms that constitute the basis for probability theory are described, and used to derive the General Law of Addition that is applied throughout statistics. Permutation and combination are introduced, leading to the concepts of sampling with and without replacement. The probability of a union of events is derived, yielding marginal and joint probabilities. Conditional probability links the joint and marginal probabiilities. Independent events yield a joint probability that is the product of the marginal probabilities. Finally, Bayes’ Theorem is derived, leading to the concepts of prior and posterior distributions in Bayesian statistics.