Probability Theory : STAT 310 / MATH 230 ; August 27 , 2013

Probability Theory : STAT 310 / MATH 230 ; Nov 27 , 2012

Probability Theory : STAT 310 / MATH 230 ; September 12 , 2010 Amir

Contents Preface 5 Chapter 1. Probability, measure and integration 7 1.1. Probability spaces, measures and σ-algebras 7 1.2. Random variables and their distribution 18 1.3. Integration and the (mathematical) expectation 30 1.4. Independence and product measures 54 Chapter 2. Asymptotics: the law of large numbers 71 2.1. Weak laws of large numbers 71 2.2. The Borel-Cantelli lemmas 77 2.3. Strong...

SYLLABUS – MCS 494: Probability on Graphs

OFFICE HOURS: 1-2 MWF. TEXT: None. I will try to point out the sections of some relevant books, which will address the corresponding material we cover. Some of these books are listed below in bibliography. PREREQUISITE: Math 310 (first course in Linear Algebra), and Stat 401 (Introduction to Probability) or equivalent courses. Basic knowledge of graphs is welcome, (some parts of MCS 261), but n...

Asymptotically efficient quantizing

[lo] H. Cramer and M. Leadbetter, “The moments of the number of [13] L. Ehrman, “Analysis of a zero-crossing frequency discriminator crossings of a level by a stationary normal process,” Ann. Math. with random inputs,” IEEE Trans. Aerospace and Navigational Stat., vol. 36, pp. 165661663, 1965. Electronics, vol. ANE-12, pp. 113-119, June 1965. [II] M. Loeve, Probability Theory. New York: Van Nos...

An algebraic framework for information theory: Classical Information

This work proposes a complete algebraic model for classical information theory. As a precursor the essential probabilistic concepts have been defined and analysed in the algebraic setting. Examples from probability and information theory demonstrate that in addition to theoretical insights provided by the algebraic model one obtains new computational and analytical tools. Several important theo...