Fundamentals of Mathematical Statistics

Probability for Statistics

AvHung T. Nguyen,Gerald S. Rogers

Inbunden, Engelska, 1989

Del i serien Springer Texts in Statistics

534 kr

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Häftad

534 kr

Häftad

534 kr

Beskrivning

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.

Produktinformation

Utgivningsdatum:1989-07-25
Mått:155 x 235 x 30 mm
Vikt:832 g
Format:Inbunden
Språk:Engelska
Serie:Springer Texts in Statistics
Antal sidor:432
Upplaga:1989
Förlag:Springer-Verlag New York Inc.
ISBN:9780387970141

Utforska kategorier

Matematisk statistik inom Naturvetenskap och teknik

Innehållsförteckning

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.