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PROBABILITY. AN INTRODUCTION 2E
Título:
PROBABILITY. AN INTRODUCTION 2E
Subtítulo:
Autor:
GRIMMETT, G
Editorial:
OXFORD UNIVERSITY PRESS
Año de edición:
2014
ISBN:
978-0-19-870997-8
Páginas:
288
36,35 €

 

Sinopsis

Directed at first and second year undergraduates
A concise introduction to probability
An honest approach to mathematical rigour
Careful choice of material, from probability to stochastic processes
Enhanced by exercises and problems
New to this Edition:
New chapter on Markov chains
Has been developed in response to the evolution of course syllabuses
Further examples, exercises, and problems including problems from the Oxford and Cambridge finals papers



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 enriched by simple exercises, together with problems (with very brief hints) many of which are taken from final examinations at Cambridge and Oxford.

The first eight chapters form a course in basic probability, being an account of events, random variables, and distributions - discrete and continuous random variables are treated separately - together with simple versions of the law of large numbers and the central limit theorem. There is an account of moment generating functions and their applications. The following three chapters are about branching processes, random walks, and continuous-time random processes such as the Poisson process. The final chapter is a fairly extensive account of Markov chains in discrete time.

This second edition develops the success of the first edition through an updated presentation, the extensive new chapter on Markov chains, and a number of new sections to ensure comprehensive coverage of the syllabi at major universities.



Part A BASIC PROBABILITY
1: Events and probabilities
2: Discrete random variables
3: Multivariate discrete distributions and independence
4: Probability generating functions
5: Distribution functions and density functions
PART B FURTHER PROBABILITY
6: Multivariate distributions and independence
7: Moments, and moment generating functions
8: The main limit theorems
9: Branching processes
10: Random walks
11: Random processes in continuous time
12: Markov chains