Basic Probability
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Primer for Data Analytics and Graduate Study in Statistics
Primer for Data Analytics and Graduate Study in Statistics
Douglas Wolfe • Grant Schneider
Primer for Data Analytics and Graduate Study in Statistics
Douglas Wolfe Department of Statistics Ohio State University Columbus, OH, USA
Grant Schneider Upstart Network, Inc. Columbus, OH, USA
ISBN 978-3-030-47478-2 ISBN 978-3-030-47479-9 https://doi.org/10.1007/978-3-030-47479-9
(eBook)
© Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Douglas Wolfe: To Robert V. Hogg and Allen T. Craig who fostered in me a passion for mathematical statistics during my graduate studies at the University of Iowa and to D. Ransom Whitney who nurtured my statistical career through my early years in academia at The Ohio State University. Grant Schneider: To my parents, Bill and Judy Schneider, who nurtured my curiosity about the world by answering my countless questions as a kid, even when they didn’t know the answers, and to Aunt Marce who gave the best, most clear-eyed advice a young man could receive, dispensed over warm Natty Lights.
Preface
For many years, we taught a summer term course for the newly entering students in our graduate programs in Statistics at Ohio State University. It was designed to refresh and/or elevate the level of understanding for the basic background in probability and distributional theory required to be successful in our Master of Applied Statistics, M.S. in Statistics, and Ph. D. programs in Statistics and Biostatistics. Over the years, this proved to be an effective way for undergraduate students from a variety of quantitative backgrounds (particularly domestic students from smaller li
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