Probability and statistics

Abstract

The text is somewhat long for complete coverage in a one-year course at the undergraduatelevelandisdesignedsothatinstructorscanmakechoicesaboutwhichtopics aremostimportanttocoverandwhichcanbeleftformorein-depthstudy.Asanexample, many instructors wish to deemphasize the classical counting arguments that are detailed in Sections 1.7–1.9. An instructor who only wants enough information to be able to cover the binomial and/or multinomial distributions can safely discuss only the definitions and theorems on permutations, combinations, and possibly multinomial coefficients. Just make sure that the students realize what these values count, otherwise the associated distributions will make no sense. The various examplesinthesesectionsarehelpful,butnotnecessary,forunderstandingtheimportant distributions. Another example is Section 3.9 on functions of two or more random variables. The use of Jacobians for general multivariate transformations might be more mathematics than the instructors of some undergraduate courses are willing to cover. The entire section could be skipped without causing problems later in the course,butsomeofthemorestraightforwardcasesearlyinthesection(suchasconvolution) might be worth introducing. The material in Sections 9.2–9.4 on optimal tests in one-parameter families is pretty mathematics, but it is of interest primarily to graduate students who require a very deep understanding of hypothesis testing theory. The rest of Chapter 9 covers everything that an undergraduate course really needs.