The Resource A first course in probability and Markov chains, Giuseppe Modica and Laura Poggiolini
A first course in probability and Markov chains, Giuseppe Modica and Laura Poggiolini
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The item A first course in probability and Markov chains, Giuseppe Modica and Laura Poggiolini represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 2 library branches.
Resource Information
The item A first course in probability and Markov chains, Giuseppe Modica and Laura Poggiolini represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 2 library branches.
 Summary

 "Provides an introduction to basic structures of probability with a view towards applications in information technology A First Course in Probability and Markov Chains presents an introduction to the basic elements in probability and focuses on two main areas. The first part explores notions and structures in probability, including combinatorics, probability measures, probability distributions, conditional probability, inclusionexclusion formulas, random variables, dispersion indexes, independent random variables as well as weak and strong laws of large numbers and central limit theorem. In the second part of the book, focus is given to Discrete Time Discrete Markov Chains which is addressed together with an introduction to Poisson processes and Continuous Time Discrete Markov Chains. This book also looks at making use of measure theory notations that unify all the presentation, in particular avoiding the separate treatment of continuous and discrete distributions. A First Course in Probability and Markov Chains: Presents the basic elements of probability. Explores elementary probability with combinatorics, uniform probability, the inclusionexclusion principle, independence and convergence of random variables. Features applications of Law of Large Numbers. Introduces Bernoulli and Poisson processes as well as discrete and continuous time Markov Chains with discrete states. Includes illustrations and examples throughout, along with solutions to problems featured in this book. The authors present a unified and comprehensive overview of probability and Markov Chains aimed at educating engineers working with probability and statistics as well as advanced undergraduate students in sciences and engineering with a basic background in mathematical analysis and linear algebra"
 "A first course in Probability and Markov Chains presents an introduction to the basic elements in statistics and focuses in two main areas"
 Language
 eng
 Extent
 1 online resource
 Contents

 Chapter 1 Combinatorics; 1.1 Binomial coefficients; 1.1.1 Pascal triangle; 1.1.2 Some properties of binomial coefficients; 1.1.3 Generalized binomial coefficients and binomial series; 1.1.4 Inversion formulas; 1.1.5 Exercises; 1.2 Sets, permutations and functions; 1.2.1 Sets; 1.2.2 Permutations; 1.2.3 Multisets; 1.2.4 Lists and functions; 1.2.5 Injective functions; 1.2.6 Monotone increasing functions; 1.2.7 Monotone nondecreasing functions; 1.2.8 Surjective functions; 1.2.9 Exercises; 1.3 Drawings; 1.3.1 Ordered drawings
 1.3.2 Simple drawings1.3.3 Multiplicative property of drawings; 1.3.4 Exercises; 1.4 Grouping; 1.4.1 Collocations of pairwise different objects; 1.4.2 Collocations of identical objects; 1.4.3 Multiplicative property; 1.4.4 Collocations in statistical physics; 1.4.5 Exercises; Chapter 2 Probability measures; 2.1 Elementary probability; 2.1.1 Exercises; 2.2 Basic facts; 2.2.1 Events; 2.2.2 Probability measures; 2.2.3 Continuity of measures; 2.2.4 Integral with respect to a measure; 2.2.5 Probabilities on finite and denumerable sets; 2.2.6 Probabilities on denumerable sets
 2.2.7 Probabilities on uncountable sets2.2.8 Exercises; 2.3 Conditional probability; 2.3.1 Definition; 2.3.2 Bayes formula; 2.3.3 Exercises; 2.4 Inclusionexclusion principle; 2.4.1 Exercises; Chapter 3 Random variables; 3.1 Random variables; 3.1.1 Definitions; 3.1.2 Expected value; 3.1.3 Functions of random variables; 3.1.4 Cavalieri formula; 3.1.5 Variance; 3.1.6 Markov and Chebyshev inequalities; 3.1.7 Variational characterization of the median and of the expected value; 3.1.8 Exercises; 3.2 A few discrete distributions; 3.2.1 Bernoulli distribution; 3.2.2 Binomial distribution
 3.2.3 Hypergeometric distribution3.2.4 Negative binomial distribution; 3.2.5 Poisson distribution; 3.2.6 Geometric distribution; 3.2.7 Exercises; 3.3 Some absolutely continuous distributions; 3.3.1 Uniform distribution; 3.3.2 Normal distribution; 3.3.3 Exponential distribution; 3.3.4 Gamma distributions; 3.3.5 Failure rate; 3.3.6 Exercises; Chapter 4 Vector valued random variables; 4.1 Joint distribution; 4.1.1 Joint and marginal distributions; 4.1.2 Exercises; 4.2 Covariance; 4.2.1 Random variables with finite expected value and variance; 4.2.2 Correlation coefficient; 4.2.3 Exercises
 4.3 Independent random variables4.3.1 Independent events; 4.3.2 Independent random variables; 4.3.3 Independence of many random variables; 4.3.4 Sum of independent random variables; 4.3.5 Exercises; 4.4 Sequences of independent random variables; 4.4.1 Weak law of large numbers; 4.4.2 BorelCantelli lemma; 4.4.3 Convergences of random variables; 4.4.4 Strong law of large numbers; 4.4.5 A few applications of the law of large numbers; 4.4.6 Central limit theorem; 4.4.7 Exercises; Chapter 5 Discrete time Markov chains; 5.1 Stochastic matrices; 5.1.1 Definitions; 5.1.2 Oriented graphs
 Isbn
 9781118477748
 Label
 A first course in probability and Markov chains
 Title
 A first course in probability and Markov chains
 Statement of responsibility
 Giuseppe Modica and Laura Poggiolini
 Language
 eng
 Summary

 "Provides an introduction to basic structures of probability with a view towards applications in information technology A First Course in Probability and Markov Chains presents an introduction to the basic elements in probability and focuses on two main areas. The first part explores notions and structures in probability, including combinatorics, probability measures, probability distributions, conditional probability, inclusionexclusion formulas, random variables, dispersion indexes, independent random variables as well as weak and strong laws of large numbers and central limit theorem. In the second part of the book, focus is given to Discrete Time Discrete Markov Chains which is addressed together with an introduction to Poisson processes and Continuous Time Discrete Markov Chains. This book also looks at making use of measure theory notations that unify all the presentation, in particular avoiding the separate treatment of continuous and discrete distributions. A First Course in Probability and Markov Chains: Presents the basic elements of probability. Explores elementary probability with combinatorics, uniform probability, the inclusionexclusion principle, independence and convergence of random variables. Features applications of Law of Large Numbers. Introduces Bernoulli and Poisson processes as well as discrete and continuous time Markov Chains with discrete states. Includes illustrations and examples throughout, along with solutions to problems featured in this book. The authors present a unified and comprehensive overview of probability and Markov Chains aimed at educating engineers working with probability and statistics as well as advanced undergraduate students in sciences and engineering with a basic background in mathematical analysis and linear algebra"
 "A first course in Probability and Markov Chains presents an introduction to the basic elements in statistics and focuses in two main areas"
 Assigning source

 Provided by publisher
 Provided by publisher
 Cataloging source
 DLC
 http://library.link/vocab/creatorName
 Modica, Giuseppe
 Dewey number
 519.2/33
 Index
 index present
 LC call number
 QA274.7
 Literary form
 non fiction
 NAL call number
 QA274.7
 NAL item number
 .M63 2013eb
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName
 Poggiolini, Laura
 http://library.link/vocab/subjectName

 Markov processes
 MATHEMATICS
 Markov processes
 Label
 A first course in probability and Markov chains, Giuseppe Modica and Laura Poggiolini
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Chapter 1 Combinatorics; 1.1 Binomial coefficients; 1.1.1 Pascal triangle; 1.1.2 Some properties of binomial coefficients; 1.1.3 Generalized binomial coefficients and binomial series; 1.1.4 Inversion formulas; 1.1.5 Exercises; 1.2 Sets, permutations and functions; 1.2.1 Sets; 1.2.2 Permutations; 1.2.3 Multisets; 1.2.4 Lists and functions; 1.2.5 Injective functions; 1.2.6 Monotone increasing functions; 1.2.7 Monotone nondecreasing functions; 1.2.8 Surjective functions; 1.2.9 Exercises; 1.3 Drawings; 1.3.1 Ordered drawings
 1.3.2 Simple drawings1.3.3 Multiplicative property of drawings; 1.3.4 Exercises; 1.4 Grouping; 1.4.1 Collocations of pairwise different objects; 1.4.2 Collocations of identical objects; 1.4.3 Multiplicative property; 1.4.4 Collocations in statistical physics; 1.4.5 Exercises; Chapter 2 Probability measures; 2.1 Elementary probability; 2.1.1 Exercises; 2.2 Basic facts; 2.2.1 Events; 2.2.2 Probability measures; 2.2.3 Continuity of measures; 2.2.4 Integral with respect to a measure; 2.2.5 Probabilities on finite and denumerable sets; 2.2.6 Probabilities on denumerable sets
 2.2.7 Probabilities on uncountable sets2.2.8 Exercises; 2.3 Conditional probability; 2.3.1 Definition; 2.3.2 Bayes formula; 2.3.3 Exercises; 2.4 Inclusionexclusion principle; 2.4.1 Exercises; Chapter 3 Random variables; 3.1 Random variables; 3.1.1 Definitions; 3.1.2 Expected value; 3.1.3 Functions of random variables; 3.1.4 Cavalieri formula; 3.1.5 Variance; 3.1.6 Markov and Chebyshev inequalities; 3.1.7 Variational characterization of the median and of the expected value; 3.1.8 Exercises; 3.2 A few discrete distributions; 3.2.1 Bernoulli distribution; 3.2.2 Binomial distribution
 3.2.3 Hypergeometric distribution3.2.4 Negative binomial distribution; 3.2.5 Poisson distribution; 3.2.6 Geometric distribution; 3.2.7 Exercises; 3.3 Some absolutely continuous distributions; 3.3.1 Uniform distribution; 3.3.2 Normal distribution; 3.3.3 Exponential distribution; 3.3.4 Gamma distributions; 3.3.5 Failure rate; 3.3.6 Exercises; Chapter 4 Vector valued random variables; 4.1 Joint distribution; 4.1.1 Joint and marginal distributions; 4.1.2 Exercises; 4.2 Covariance; 4.2.1 Random variables with finite expected value and variance; 4.2.2 Correlation coefficient; 4.2.3 Exercises
 4.3 Independent random variables4.3.1 Independent events; 4.3.2 Independent random variables; 4.3.3 Independence of many random variables; 4.3.4 Sum of independent random variables; 4.3.5 Exercises; 4.4 Sequences of independent random variables; 4.4.1 Weak law of large numbers; 4.4.2 BorelCantelli lemma; 4.4.3 Convergences of random variables; 4.4.4 Strong law of large numbers; 4.4.5 A few applications of the law of large numbers; 4.4.6 Central limit theorem; 4.4.7 Exercises; Chapter 5 Discrete time Markov chains; 5.1 Stochastic matrices; 5.1.1 Definitions; 5.1.2 Oriented graphs
 Control code
 813568123
 Extent
 1 online resource
 Form of item
 online
 Isbn
 9781118477748
 Lccn
 2012042679
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 http://library.link/vocab/ext/overdrive/overdriveId

 cl0500000305
 addc87cefb5a45d68afcc921e43c8f86
 Publisher number
 EB00063713
 Specific material designation
 remote
 System control number
 (OCoLC)813568123
 Label
 A first course in probability and Markov chains, Giuseppe Modica and Laura Poggiolini
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Chapter 1 Combinatorics; 1.1 Binomial coefficients; 1.1.1 Pascal triangle; 1.1.2 Some properties of binomial coefficients; 1.1.3 Generalized binomial coefficients and binomial series; 1.1.4 Inversion formulas; 1.1.5 Exercises; 1.2 Sets, permutations and functions; 1.2.1 Sets; 1.2.2 Permutations; 1.2.3 Multisets; 1.2.4 Lists and functions; 1.2.5 Injective functions; 1.2.6 Monotone increasing functions; 1.2.7 Monotone nondecreasing functions; 1.2.8 Surjective functions; 1.2.9 Exercises; 1.3 Drawings; 1.3.1 Ordered drawings
 1.3.2 Simple drawings1.3.3 Multiplicative property of drawings; 1.3.4 Exercises; 1.4 Grouping; 1.4.1 Collocations of pairwise different objects; 1.4.2 Collocations of identical objects; 1.4.3 Multiplicative property; 1.4.4 Collocations in statistical physics; 1.4.5 Exercises; Chapter 2 Probability measures; 2.1 Elementary probability; 2.1.1 Exercises; 2.2 Basic facts; 2.2.1 Events; 2.2.2 Probability measures; 2.2.3 Continuity of measures; 2.2.4 Integral with respect to a measure; 2.2.5 Probabilities on finite and denumerable sets; 2.2.6 Probabilities on denumerable sets
 2.2.7 Probabilities on uncountable sets2.2.8 Exercises; 2.3 Conditional probability; 2.3.1 Definition; 2.3.2 Bayes formula; 2.3.3 Exercises; 2.4 Inclusionexclusion principle; 2.4.1 Exercises; Chapter 3 Random variables; 3.1 Random variables; 3.1.1 Definitions; 3.1.2 Expected value; 3.1.3 Functions of random variables; 3.1.4 Cavalieri formula; 3.1.5 Variance; 3.1.6 Markov and Chebyshev inequalities; 3.1.7 Variational characterization of the median and of the expected value; 3.1.8 Exercises; 3.2 A few discrete distributions; 3.2.1 Bernoulli distribution; 3.2.2 Binomial distribution
 3.2.3 Hypergeometric distribution3.2.4 Negative binomial distribution; 3.2.5 Poisson distribution; 3.2.6 Geometric distribution; 3.2.7 Exercises; 3.3 Some absolutely continuous distributions; 3.3.1 Uniform distribution; 3.3.2 Normal distribution; 3.3.3 Exponential distribution; 3.3.4 Gamma distributions; 3.3.5 Failure rate; 3.3.6 Exercises; Chapter 4 Vector valued random variables; 4.1 Joint distribution; 4.1.1 Joint and marginal distributions; 4.1.2 Exercises; 4.2 Covariance; 4.2.1 Random variables with finite expected value and variance; 4.2.2 Correlation coefficient; 4.2.3 Exercises
 4.3 Independent random variables4.3.1 Independent events; 4.3.2 Independent random variables; 4.3.3 Independence of many random variables; 4.3.4 Sum of independent random variables; 4.3.5 Exercises; 4.4 Sequences of independent random variables; 4.4.1 Weak law of large numbers; 4.4.2 BorelCantelli lemma; 4.4.3 Convergences of random variables; 4.4.4 Strong law of large numbers; 4.4.5 A few applications of the law of large numbers; 4.4.6 Central limit theorem; 4.4.7 Exercises; Chapter 5 Discrete time Markov chains; 5.1 Stochastic matrices; 5.1.1 Definitions; 5.1.2 Oriented graphs
 Control code
 813568123
 Extent
 1 online resource
 Form of item
 online
 Isbn
 9781118477748
 Lccn
 2012042679
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 http://library.link/vocab/ext/overdrive/overdriveId

 cl0500000305
 addc87cefb5a45d68afcc921e43c8f86
 Publisher number
 EB00063713
 Specific material designation
 remote
 System control number
 (OCoLC)813568123
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