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# Probability : an introduction

Author: Geoffrey Grimmett; D J A Welsh Oxford : Oxford University Press, [2014] ©2014 eBook : Document : English : Second editionView all editions and formats Probability 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 en.  Read more... (not yet rated) 0 with reviews - Be the first.

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Genre/Form: Electronic books Print version:Grimmett, Geoffrey.Probability.Oxford : Oxford University Press, 2014 Document, Internet resource Internet Resource, Computer File Geoffrey Grimmett; D J A Welsh Find more information about: Geoffrey Grimmett D J A Welsh 9780191019920 0191019925 9781322336381 1322336385 891447200 1 online resource (x, 270 pages) : illustrations Cover; 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. 3 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. 5.4 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. 7.1 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 Cramér'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. 9.6 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. Geoffrey Grimmett, Dominic Welsh.

### Abstract:

Probability 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  Read more...

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"This book is an updated version of the 1986 classic... There is a new chapter on Markov chains, and a few new sections and problems, but the book still retains its concise, direct style." --MAA Read more...

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