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Fundamentals of Mathematical Statistics Probability for Statistics

Nguyen Hung T. Rogers Gerald S.
Innbundet / 1989 / Engelsk

Produktdetaljer

ISBN
9780387970141
Publisert
1989-07-25
Utgiver
Vendor
Springer-Verlag New York Inc.
Høyde
235 mm
Bredde
155 mm
Aldersnivå
Graduate, P, 06
Språk
Product language
Engelsk
Format
Product format
Innbundet

Forfatter
Nguyen Hung T.
Rogers Gerald S.

Fundamentals of Mathematical Statistics Probability for Statistics

Nguyen Hung T. Rogers Gerald S.
Innbundet / 1989 / Engelsk
Nguyen Hung T. Rogers Gerald S.
Innbundet / 1989 / Engelsk
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This is the first half of a text for a 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. We suggest that the following distinguish this text from other introductions to mathematical statistics. 1. The most obvious thing is the layout. We have designed each lesson for the (U.S.) 50 minute class; those who study independently probably need the traditional three hours for each lesson. Since we have more than (the U.S. again) 90 lessons, some choices have to be made. In the table of contents, we have used a * to designate those lessons which are "interesting but not essential" (INE) and may be omitted from a general course; some exercises and proofs in other lessons are also "INE". We have made lessons of some material which other writers might stuff into appendices. Incorporating this freedom of choice has led to some redundancy, mostly in definitions, which may be beneficial.
Les mer
This is the first half of a text for a 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.
Les mer
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.
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GPSR Compliance The European Union's (EU) General Product Safety Regulation (GPSR) is a set of rules that requires consumer products to be safe and our obligations to ensure this. If you have any concerns about our products you can contact us on ProductSafety@springernature.com. In case Publisher is established outside the EU, the EU authorized representative is: Springer Nature Customer Service Center GmbH Europaplatz 3 69115 Heidelberg, Germany ProductSafety@springernature.com
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This is the first half of a text for a 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. We suggest that the following distinguish this text from other introductions to mathematical statistics. 1. The most obvious thing is the layout. We have designed each lesson for the (U.S.) 50 minute class; those who study independently probably need the traditional three hours for each lesson. Since we have more than (the U.S. again) 90 lessons, some choices have to be made. In the table of contents, we have used a * to designate those lessons which are "interesting but not essential" (INE) and may be omitted from a general course; some exercises and proofs in other lessons are also "INE". We have made lessons of some material which other writers might stuff into appendices. Incorporating this freedom of choice has led to some redundancy, mostly in definitions, which may be beneficial.
Les mer
This is the first half of a text for a 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.
Les mer
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.
Les mer
Springer Book Archives
GPSR Compliance The European Union's (EU) General Product Safety Regulation (GPSR) is a set of rules that requires consumer products to be safe and our obligations to ensure this. If you have any concerns about our products you can contact us on ProductSafety@springernature.com. In case Publisher is established outside the EU, the EU authorized representative is: Springer Nature Customer Service Center GmbH Europaplatz 3 69115 Heidelberg, Germany ProductSafety@springernature.com
Les mer

Produktdetaljer

ISBN
9780387970141
Publisert
1989-07-25
Utgiver
Vendor
Springer-Verlag New York Inc.
Høyde
235 mm
Bredde
155 mm
Aldersnivå
Graduate, P, 06
Språk
Product language
Engelsk
Format
Product format
Innbundet

Forfatter
Nguyen Hung T.
Rogers Gerald S.

Relaterte produkter