Jump to ContentJump to Main Navigation
Random Processes in Physics and Finance$
Users without a subscription are not able to see the full content.

Melvin Lax, Wei Cai, and Min Xu

Print publication date: 2006

Print ISBN-13: 9780198567769

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198567769.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2017. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in OSO for personal use (for details see http://www.oxfordscholarship.com/page/privacy-policy).date: 22 April 2018

Review of probability

Review of probability

Chapter:
(p.1) 1 Review of probability
Source:
Random Processes in Physics and Finance
Author(s):

Melvin Lax

Wei Cai

Min Xu

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198567769.003.0001

This chapter reviews probability theory, limiting the discussion to the study of random events as opposed to random processes, the latter being a sequence of random events extended over a period of time. The goal is to raise the level of approach by demonstrating the usefulness of delta functions. The chapter presents a calculation of the chi-squared distribution (important in statistical decision making) with delta functions. The normalisation condition of the probability density in chi-square leads to a geometric result; namely, the volume of a sphere in n dimensions can be determined without ever transferring to spherical coordinates. This chapter also discusses the first and second laws of gambling, along with distribution functions, stochastic variables, expectation values for single random variables, characteristic functions and generating functions, measures of dispersion, joint events, conditional probabilities and Bayes' theorem, sums of random variables, fitting of experimental observations, and multivariate normal distributions.

Keywords:   probability theory, random events, delta functions, laws of gambling, distribution functions, stochastic variables, characteristic functions, generating functions, dispersion, joint events

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .