LEADER 05266nam 2200649 450 001 9910816205203321 005 20230803205241.0 010 $a0-19-101993-3 010 $a0-19-870996-X 010 $a0-19-101992-5 035 $a(CKB)3710000000244179 035 $a(EBL)1791152 035 $a(SSID)ssj0001377143 035 $a(PQKBManifestationID)11875099 035 $a(PQKBTitleCode)TC0001377143 035 $a(PQKBWorkID)11327329 035 $a(PQKB)11178082 035 $a(MiAaPQ)EBC1791152 035 $a(Au-PeEL)EBL1791152 035 $a(CaPaEBR)ebr10935430 035 $a(CaONFJC)MIL664920 035 $a(OCoLC)891447200 035 $a(EXLCZ)993710000000244179 100 $a20141009h20142014 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aProbability $ean introduction /$fGeoffrey Grimmett, Dominic Welsh 205 $aSecond edition. 210 1$aOxford, [England] :$cOxford University Press,$d2014. 210 4$dİ2014 215 $a1 online resource (281 p.) 300 $aDescription based upon print version of record. 311 $a1-322-33638-5 311 $a0-19-870997-8 320 $aIncludes bibliographical references and index. 327 $aCover; Preface to the second edition; Contents; Part A Basic Probability; 1 Events and probabilities; 1.1 Experiments with chance; 1.2 Outcomes and events; 1.3 Probabilities; 1.4 Probability spaces; 1.5 Discrete sample spaces; 1.6 Conditional probabilities; 1.7 Independent events; 1.8 The partition theorem; 1.9 Probability measures are continuous; 1.10 Worked problems; 1.11 Problems; 2 Discrete random variables; 2.1 Probability mass functions; 2.2 Examples; 2.3 Functions of discrete random variables; 2.4 Expectation; 2.5 Conditional expectation and the partition theorem; 2.6 Problems 327 $a3 Multivariate discrete distributions and independence3.1 Bivariate discrete distributions; 3.2 Expectation in the multivariate case; 3.3 Independence of discrete random variables; 3.4 Sums of random variables; 3.5 Indicator functions; 3.6 Problems; 4 Probability generating functions; 4.1 Generating functions; 4.2 Integer-valued random variables; 4.3 Moments; 4.4 Sums of independent random variables; 4.5 Problems; 5 Distribution functions and density functions; 5.1 Distribution functions; 5.2 Examples of distribution functions; 5.3 Continuous random variables 327 $a5.4 Some common density functions5.5 Functions of random variables; 5.6 Expectations of continuous random variables; 5.7 Geometrical probability; 5.8 Problems; Part B Further Probability; 6 Multivariate distributions and independence; 6.1 Random vectors and independence; 6.2 Joint density functions; 6.3 Marginal density functions and independence; 6.4 Sums of continuous random variables; 6.5 Changes of variables; 6.6 Conditional density functions; 6.7 Expectations of continuous random variables; 6.8 Bivariate normal distribution; 6.9 Problems; 7 Moments, and moment generating functions 327 $a7.1 A general note7.2 Moments; 7.3 Variance and covariance; 7.4 Moment generating functions; 7.5 Two inequalities; 7.6 Characteristic functions; 7.7 Problems; 8 The main limit theorems; 8.1 The law of averages; 8.2 Chebyshev's inequality and the weak law; 8.3 The central limit theorem; 8.4 Large deviations and Cram ?er's theorem; 8.5 Convergence in distribution, and characteristic functions; 8.6 Problems; Part C Random Processes; 9 Branching processes; 9.1 Random processes; 9.2 A model for population growth; 9.3 The generating-function method; 9.4 An example; 9.5 The probability of extinction 327 $a9.6 Problems10 Random walks; 10.1 One-dimensional random walks; 10.2 Transition probabilities; 10.3 Recurrence and transience of random walks; 10.4 The Gambler's Ruin Problem; 10.5 Problems; 11 Random processes in continuous time; 11.1 Life at a telephone switchboard; 11.2 Poisson processes; 11.3 Inter-arrival times and the exponential distribution; 11.4 Population growth, and the simple birth process; 11.5 Birth and death processes; 11.6 A simple queueing model; 11.7 Problems; 12 Markov chains; 12.1 The Markov property; 12.2 Transition probabilities; 12.3 Class structure 327 $a12.4 Recurrence and transience 330 $aProbability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour. This book is a compact account of the basic features of probability and random processes at the level of first and second year mathematics undergraduates and Masters'' students in cognate fields. It is suitable for a first course in probability, plus a follow-up course in random processes including Markov chains.A special feature is the authors'' attention to rigorous mathematics: not everything is rigorous, but the need for rigour is explained at difficult junctures. The text is 606 $aProbabilities 615 0$aProbabilities. 676 $a519.2 700 $aGrimmett$b Geoffrey$0265888 702 $aWelsh$b D. J. A. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910816205203321 996 $aProbability$94003269 997 $aUNINA