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      PROBABILITY

      With Applications and R

       Second Edition

       AMY S. WAGAMAN

      Department of Mathematics and Statistics

      Amherst College

      Amherst, MA

       ROBERT P. DOBROW

      Department of Mathematics

      Carleton College

      Northfield, MN

      This edition first published 2021

      © 2021 John Wiley & Sons, Inc.

      Edition History John Wiley & Sons, Inc. (1e, 2014)

      All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.

      The rights of Amy S. Wagaman and Robert P. Dobrow to be identified as the authors of this work has been asserted in accordance with law.

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      The contents of this work are intended to further general scientific research, understanding, and discussion only and are not intended and should not be relied upon as recommending or promoting scientific method, diagnosis, or treatment by physicians for any particular patient. In view of ongoing research, equipment modifications, changes in governmental regulations, and the constant flow of information relating to the use of medicines, equipment, and devices, the reader is urged to review and evaluate the information provided in the package insert or instructions for each medicine, equipment, or device for, among other things, any changes in the instructions or indication of usage and for added warnings and precautions. While the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

       Library of Congress Cataloging-in-Publication Data

      Names: Wagaman, Amy Shepherd, 1982- author. | Dobrow, Robert P., author.

      Title: Probability : with applications and R / Amy S. Wagaman, Department of Mathematics and Statistics, Amherst College, Amherst, MA, Robert P. Dobrow, Department of Mathematics, Carleton College, Northfield, MN.

      Description: Second edition. | Hoboken, NJ : Wiley, [2021] | Includes bibliographical references and index.

      Identifiers: LCCN 2021007900 (print) | LCCN 2021007901 (ebook) | ISBN 9781119692386 (cloth) | ISBN 9781119692348 (adobe pdf) | ISBN 9781119692416 (epub)

      Subjects: LCSH: Probabilities–Data processing. | R (Computer program language)

      Classification: LCC QA276.45.R3 D63 2021 (print) | LCC QA276.45.R3 (ebook) | DDC 519.20285/5133–dc23

      LC record available at https://lccn.loc.gov/2021007900

      LC ebook record available at https://lccn.loc.gov/2021007901

      Cover Design: Wiley

      Cover Image: © D3Damon/Getty Images, NicoElNino/Shutterstock

       Amy: To my fantastic, supportive fiancé, Stephen,my beloved parents (rest in peace, Mom), and my Aunt Pat

       Bob: To my wonderful familyAngel, Joe, Danny, Tom

      Probability: With Applications and R is a probability

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