Chapter 29 – Probability

Publisher Summary This chapter highlights the information available in Mathematica about most standard probability distributions. For each distribution, cumulative distribution function, probability density function, quantiles, mean, variance, and random numbers can be achieved. As examples of discrete, continuous, and multivariate distributions, the chapter considers the binomial, multinomial, normal, and bivariate normal distributions in detail. One very useful property of Mathematica is the ease of random number generation. By default, a cellular-automata-based random number generator called “ExtendedCA” is used. According to the documentation, this generator produces an extremely high level of randomness. This makes it very convenient to perform simulations. A variety of processes are simulated, from a simple random walk to coin tossing, gambler's ruin, Brownian motion, discrete-time Markov process, Poisson process, birth-death process, and M/M/1 queue. From these simulations, the realizations of the processes are displayed.