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Discrete Probability: Lecture Slide Notes by Ralph E. Morganstern

Discrete Probability: Lecture Slide Notes

by Ralph E. Morganstern
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Book cover type: Paperback
  • ISBN13: 9781481282062
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Createspace Independent Publishing Platform
  • Publisher Imprint: Createspace Independent Publishing Platform
  • Publication Date:
  • Pages: 180
  • Original Price: USD 15.0
  • Language: English
  • Edition: N/A
  • Item Weight: 318 grams
  • BISAC Subject(s): Probability & Statistics / General

These Lecture Slide Notes have been used for a two-quarter graduate level sequence in probability covering discrete and continuous probability in two separate volumes. Although reasonably self-contained, they do not constitute a formal exposition on the subject; rather the intent is to provide a concise and accessible format for reference and self-study. In this regard, each slide stands alone to encapsulate a complete concept, algorithm, or theorem, using a combination of equations, graphs, diagrams, and comparison tables. The explanatory notes are placed directly below each slide in order to reinforce key concepts and give additional insights. A Table of Contents serves to organize the slides by topic and gives a complete list of slide titles and their page numbers. An index is also provided in order to link related aspects of topics and also to cross-reference key concepts, specific applications, and the abundant visual aids.This book constitutes the first volume on discrete probability; a second volume will cover continuous probability. Part 1 covers counting with and without replacement, axiomatic probability models, computation techniques, conditional, joint, marginal, and Bayesian update probabilities. The concept of a random variable (RV) is fully characterized by a discrete probability mass function (PMF) and a quasi-continuous cumulative distribution function (CDF). A numerical characterization of a RV is given by the mean, variance, and expectation value. Pairs of RVs give way to new concepts such as independence, covariance, and the effects of linear and bi-linear transformations. Common discrete probability mass functions (PMFs) are discussed in terms of related pairs, tree diagrams, and algebraic representations.

The author is an adjunct lecturer at Santa Clara University, Santa Clara, CA and is currently teaching a sequence in probability and in numerical analysis for engineering graduate students. Over the years he has taught both undergraduate and graduate courses in physics and mathematics while performing research in general relativity, astrophysics, and cosmology, and more recently in applying fundamental physics to problems in the aerospace industry. He received a B.S. in Mathematics from Rensselaer Polytechnic Institute, Troy, N.Y., and an M.A. and Ph.D. in Physics from the State University of New York in Stony Brook, N.Y.

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