07810cam a2200853 i 4500 ocn813568123 OCoLC 20171113140734.0 m o d cr ||||||||||| 121018s2013 enk ob 001 0 eng 2012042679 9781118477748 (ePub) 111847774X (ePub) 9781118477809 (Adobe PDF) 1118477804 (Adobe PDF) 9781118477816 (MobiPocke) 1118477812 (MobiPocke) 9781118477793 (electronic bk.) 1118477790 (electronic bk.) 9781119944874 (hardback) 9781299188280 1299188281 1119944872 (hardback) EB00063713 Recorded Books AU@ 000050562216 AU@ 000052162463 CHNEW 000600026 DEBBG BV041432883 DEBSZ 39747590X DEBSZ 398288275 DEBSZ 43133241X NZ1 15351000 NZ1 16175229 DEBSZ 452512662 DEBBG BV043395134 (OCoLC)813568123 (OCoLC)827207583 (OCoLC)859157030 (OCoLC)864913652 (OCoLC)880597009 (OCoLC)966465300 CL0500000305 Safari Books Online ADDC87CE-FB5A-45D6-8AFC-C921E43C8F86 OverDrive, Inc. http://www.overdrive.com DLC eng rda pn DLC YDX DG1 N$T YDXCP E7B UBY COO NOC UMI DEBSZ TEFOD OCLCF RECBK EBLCP MHW TEFOD OCLCQ VT2 CDS pcc MAIN QA274.7 MAT 029040 bisacsh 519.2/33 23 MAT029000 bisacsh Modica, Giuseppe. A first course in probability and Markov chains / Giuseppe Modica and Laura Poggiolini. [electronic resource] Chichester : Wiley, 2013. 1 online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references and index. 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. "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"-- Provided by publisher. "A first course in Probability and Markov Chains presents an introduction to the basic elements in statistics and focuses in two main areas"-- Provided by publisher. Print version record and CIP data provided by publisher. Markov processes. Markov processes. MATHEMATICS Probability & Statistics General. bisacsh Markov processes. fast (OCoLC)fst01010347 Markov processes. local Electronic books. Electronic books. Poggiolini, Laura. Print version: Modica, Giuseppe. First course in probability and Markov chains 9781119944874 (DLC) 2012033463 http://onlinelibrary.wiley.com/book/10.1002/9781118477793 Wiley Online Library ddc BK 206225 206225