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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

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
Creator
Contributor
Subject
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, inclusion-exclusion 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 inclusion-exclusion 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
Instantiates
Publication
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 Inclusion-exclusion 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 Borel-Cantelli 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
9781118477793
Lccn
2012042679
Media category
computer
Media MARC source
rdamedia
Media type code
c
http://library.link/vocab/ext/overdrive/overdriveId
  • cl0500000305
  • addc87ce-fb5a-45d6-8afc-c921e43c8f86
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
Publication
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 Inclusion-exclusion 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 Borel-Cantelli 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
9781118477793
Lccn
2012042679
Media category
computer
Media MARC source
rdamedia
Media type code
c
http://library.link/vocab/ext/overdrive/overdriveId
  • cl0500000305
  • addc87ce-fb5a-45d6-8afc-c921e43c8f86
Publisher number
EB00063713
Specific material designation
remote
System control number
(OCoLC)813568123

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