Fundamentals of Mathematical Statistics: Probability for Statistics

ISBN-13: 9781461269847 / Angielski / Miękka / 2012 / 432 str.

Hung T. Nguyen; Gerald S. Rogers

Opis

This is the first half of a set of lecture notes with exercises - a text - for two semester course in mathematical statistics at the senior/graduate level for those who need a strong background in statistics as an essential tool in their career. To study this text, the reader needs a thorough familiarity with calculus including such things as Jacobians and series but somewhat less intense familiarity with matrices including quadratic forms and eigenvalues. For convenience, these lecture notes were divided into two parts: "Volume I, Probability for Statistics," for the first semester, and "Volume II, Statistical Inference, " for the second.

Spis treści

I:Elementary Probability and Statistics.- 1 Relative frequency.- 2 Sample spaces.- * 3 Some rules about sets (see footnote).- 4 The counting function for finite sets.- 5 Probability on finite sample spaces.- * 6 Ordered selections.- * 7 Unordered selections.- 8 Some uniform probability spaces.- 9 Conditional probability/independence.- * 10 Bayes’ rule.- 11 Random variables.- 12 Expectation.- 13 A hypergeometric distribution.- * 14 Sampling and simulation.- 15 Testing simple hypotheses.- * 16 An acceptance sampling plan.- 17 The binomial distribution.- * 18 Matching and catching.- 19 Confidence intervals for a Bernoulli ?.- 20 The Poisson distribution.- * 21 The negative binomial distribution.- II:Probability and Expectation.- 1 Some set theory.- 2 Basic probability theory.- 3 The cumulative distribution function.- 4 Some continuous CDFs.- 5 The normal distribution.- 6 Some algebra of random variables.- 7 Convergence of sequences of random variables.- 8 Convergence almost surely and in probability.- 9 Integration-I.- * 10 Integration-II.- 11 Theorems for expectation.- 12 Stieltjes integrals.- 13 Product measures and integrals.- III:Limiting Distributions.- 1 Joint distributions: discrete.- 2 Conditional distributions: discrete.- 3 Joint distributions: continuous.- 4 Conditional distributions: continuous.- 5 Expectation: examples.- 6 Convergence in mean, in distribution.- * 7 Other relations in modes of convergence.- 8 Laws of large numbers.- 9 Convergence of sequences of distribution functions.- 10 Convergence of sequences of integrals.- 11 On the sum of random variables.- 12 Characteristic functions-I.- 13 Characteristic functions-II.- 14 Convergence of sequences of characteristic functions.- 15 Central limit theorems.- References.

O autorze

Hung T. Nguyen is a professor of Mathematical Sciences at New Mexico State University, USA.