Appendix A: Probability and Statistics Overview
James V. Candy · 2008
Defining a sample space (outcomes), , a field (events), B, and a probability function (on a class of events), Pr, we can construct an experiment as the triple, { , B, Pr}. Example A.1Consider the experiment, { , B, Pr} of tossing a fair coin, then we see that Sample space: = {H, T } Events: B = {0, {H}, {T }} Probability:Pr(H) = p Pr(T ) = 1p With the idea of a sample space, probability function, and experiment in mind, we can now start to define the concept of a discrete random signal more precisely.We define a discrete random variable as a real function whose value is determined by the outcome of an experiment.It assigns a real number to each point of a sample space , which consists of all the possible outcomes of the experiment.A random variable X and its realization x are written as X(ω) = x for ω (A.1)Consider the following example of a simple experiment. Bayesian Signal Processing.By James V. Candy