Arak M. Mathai - Probability and Statistics: A Course for Physicists and Engineers

Arak M. Mathai and Hans J. Haubold

Probability and Statistics

De Gruyter Textbook

Linear Algebra. A Course for Physicists and Engineers

Arak M. Mathai, Hans J. Haubold, 2017

ISBN 978-3-11-056235-4, e-ISBN (PDF) 978-3-11-056250-7,

e-ISBN (EPUB) 978-3-11-056259-0

Probability Theory and Statistical Applications .

A Profound Treatise for Self-Study

Peter Zrnig, 2016

ISBN 978-3-11-036319-7, e-ISBN (PDF) 978-3-11-040271-1,

e-ISBN (EPUB) 978-3-11-040283-4

Brownian Motion. An Introduction to Stochastic Processes

Ren L. Schilling, Lothar Partzsch, 2014

ISBN 978-3-11-030729-0, e-ISBN (PDF) 978-3-11-030730-6,

e-ISBN (EPUB) 978-3-11-037398-1

Numerical Analysis of Stochastic Processes

Wolf-Jrgen Beyn, Raphael Kruse, 2018

ISBN 978-3-11-044337-0, e-ISBN (PDF) 978-3-11-044338-7,

e-ISBN (EPUB) 978-3-11-043555-9

Compressive Sensing .

Applications to Sensor Systems and Image Processing

Joachim Ender, 2018

ISBN 978-3-11-033531-6, e-ISBN (PDF) 978-3-11-033539-2,

e-ISBN (EPUB) 978-3-11-039027-8

Mathematics Subject Classification 2010

60-00, 60-01, 60A05, 60D05, 60E05, 62-00, 62-01, 62P30, 62P35

Authors

Prof. Dr. Arak M. Mathai

McGill University

Department of Mathematics and Statistics

805 Sherbrooke St. West

Montreal, QC H3A 2K6

Canada

Prof. Dr. Hans J. Haubold

United Nations Office for Outer Space Afairs

Vienna International Centre

P.O. Box 500

1400 Vienna

Austria

ISBN 978-3-11-056253-8

e-ISBN (PDF) 978-3-11-056254-5

e-ISBN (EPUB) 978-3-11-056260-6

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0

License. For details go to http://creativecommons.org/licenses/by-nc-nd/4.0/.

Library of Congress Cataloging-in-Publication Data

A CIP catalog record for this book has been applied for at the Library of Congress.

Bibliographic information published by the Deutsche Nationalbibliothek

The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie;

detailed bibliographic data are available on the Internet at http://dnb.dnb.de.

2018 Arak M. Mathai, Hans J. Haubold, published by Walter de Gruyter GmbH, Berlin/Boston.

The book is published with open access at www.degruyter.com.

Cover image: Pasieka, Alfred / Science Photo Library

www.degruyter.com

Due to great interest shown by students, a proposal was made to the Department of Science and Technology, Government of India, New Delhi, India (DST), for conducting a sequence of 10-day mathematics camps for undergraduates during holidays so that in one sequence of four camps the essential basic mathematics could be covered. DST approved this project with full financial support for 30 candidates in each camp. Principals of colleges in Kerala, India, were asked to select up to 5 motivated students from each college. The camp is run at CMSS from 08:30 am until 6:00 pm, continuously for 10 days of nearly 40 hours of lectures and 40 hours of problem-solving sessions. In one camp, Modules 1, 2, 3, on basic linear algebra for all disciplines, are covered. In a second camp, Modules 4 and 5, covering the topics of sequences, limits, continuity and differential calculus and the basic integral calculus, are covered. In a third camp, Module 6, covering the topics of sample space, probability, random variables, expected values, statistical distributions and their applications, are covered. In the fourth camp, Modules 7 and 9, covering the topics of sampling distributions, statistical inference, prediction and model building, design of experiments and some non-parametric tests, are covered.

The basic sequence of four camps, covering basic mathematics, probability and statistics, were repeated over the years from 2007 to 2014. There were also a four to six weeks course every year at the research level, meant for MSc and PhD students, and young faculty, known as SERC (Science and Engineering Research Council of the Department of Science and Technology, Government of India, New Delhi) Schools. The notes from these schools were brought out by CMSS in book form every year. Selected notes from the SERC schools of 1995 to 2006 was brought out as Special Functions for Applied Scientists by Springer, New York in 2008, authored by A. M. Mathai and Hans J. Haubold. Selected notes from the SERC Schools of 2007 to 2012 appeared in 2017 as a research level book by Springer, New York. Selected notes from the SERC Schools of 2013 to 2015 will appear as a research level book on Matrix Methods and Fractional Calculus by World Scientific Publishing, all by the same authors.

The present book on probability and statistics consists of 16 chapters. covering the topic of sampling distributions, point estimation, interval estimation, tests of hypotheses, prediction, regression and model building problems, design of experiments and analysis of variance, some non-parametric tests, questions and answers.

All concepts in probability and statistics are explained properly and illustrated with real-life examples. The material is developed slowly so that the book can be used as a self-study material also. Proper interpretations of the concepts of variance, covariance, correlation, multiple correlation, a statistical hypothesis, meaning of tests of a statistical hypothesis, difference between regression and correlation analysis, difference between prediction and model building, etc. are given. An introduction to matrix-variate distributions such as matrix-variate Gaussian, matrix-variate gamma and matrix-variate beta are also given.

Since 2004, the material in this book was made available to UN-afiliated Regional Centres for Space Science and Technology Education, located in India, China, Morocco, Nigeria, Jordan, Brazil and Mexico (http://www.unoosa.org/oosa/en/ourwork/psa/regional-centres/index.html).

Since 1988, the material was taken into account for the development of education curricula in the fields of remote sensing and geographic information systems, satellite meteorology and global climate, satellite communications, space and atmospheric science and global navigation satellite systems (http://www.unoosa.org/oosa/en/ourwork/psa/regional-centres/study_curricula.html).