ABSTRACT
The theory of probability and mathematical statistics is a very important branch in experimental sciences. The solutions to probability and mathematical statistics problems sometimes could be quite involved. The traditional statistics usually relies heavily on lookup-tables. A very comprehensive statistics toolbox is provided in MATLAB which contains a lot of handy functions for solving related probability and mathematical statistics problems. In Section 9.1, the basic concepts of probability density function (PDF) and cumulative distribution function (CDF) are introduced. Given probability distributions, various probability related example problems are solved using Statistics Toolbox. In this section, pseudo-random number generators of different distributions, such as uniform distribution, normal distribution, Poisson distribution, etc., are introduced and demonstrated. In Section 9.2, how to compute statistical quantities, such as mean, variance, moments and covariances is covered for both univariate and multivariate distributions together with an introduction to Monte Carlo method and its applications. The parametric estimation and interval estimation problems, together with their MATLAB implementations, are given in Section 9.3 where multi-variable linear regression and least squares data fitting problems are also presented. In Section 9.4, the hypothesis test problems including mean value test, normality test and given distribution test, are discussed. The variance analysis problems and applications are presented in Section 9.5 with detailed example solutions in MATLAB.
