Mathematical Statistics PDF
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Moment- Generating Distribution Probability Function Mean Variance Function Uniform f (y) = 1 θ2 − θ1 ; θ1 ≤ y ≤ θ2 θ1 + θ2 2 (θ2 − θ1)2 12 etθ2 − etθ1 t(θ2 − θ1) Normal f (y) = 1 σ √ 2π exp � − � 1 2σ 2 � (y − µ)2 � µ σ 2 + t2σ 2 2 � −∞ < y < +∞ Exponential f (y) = 1 β e−y/β; β > 0 β β2 (1 − βt)−1 0 < y < ∞ Gamma f (y) = � 1 �(α)βα � yα−1e−y/β; αβ αβ2 (1 − βt)−α 0 < y < ∞ Chi-square f (y) = (y)(v/2)−1e−y/2 2v/2�(v/2) ; v 2v (1−2t)−v/2 y2 > 0 Beta f (y) = � �(α + β) �(α)�(β) � yα−1(1 − y)β−1; α α + β αβ (α + β)2(α + β + 1) does not exist in closed form 0 < y < 1 Continuous Distributions exp µt Moment- Generating Distribution Probability Function Mean Variance Function Binomial p(y) = � n y � py(1 − p)n−y; np np(1 − p) [pet + (1 − p)]n y = 0, 1, . . . , n Geometric p(y) = p(1 − p)y−1; 1 p 1 − p p2 pet 1 − (1 − p)et y = 1, 2, . . . Hypergeometric p(y) = � r y � � N−r n−y � � N n � ; nr N n � r N � � N − r N � � N − n N − 1 � y = 0, 1, . . . , n if n ≤ r, y = 0, 1, . . . , r if n > r Poisson p(y) = λye−λ y! ; λ λ exp[λ(et − 1)] y = 0, 1, 2, . . . Negative binomial p(y) = � y−1 r−1 � pr(1 − p)y−r; r p r(1 − p) p2 � pet 1 − (1 − p)et �r y = r, r + 1, . . . Discrete Distributions M A T H E M A T I C A L S T A T I S T I C S W I T H A P P L I C A T I O N S This page intentionally left blank S E V E N T H E D I T I O N Mathematical Statistics with Applications Dennis D. Wackerly University of Florida William Mendenhall III University of Florida, Emeritus Richard L. Scheaffer University of Florida, Emeritus Australia • Brazil • Canada • Mexico • Singapore • Spain United Kingdom • United States Mathematical Statistics with Applications, Seventh Edition Dennis D. Wackerly, William Mendenhall III, Richard L. Scheaffer Statistics Editor: Carolyn Crockett Assistant Editors: Beth Gershman, Catie Ronquillo Editorial Assistant: Ashley Summers Technology Project Manager: Jennifer Liang Marketing Manager: Mandy Jellerichs Marketing Assistant: Ashley Pickering Marketing Communications Manager: Darlene Amidon-Brent Project Manager, Editorial Production: Hal Humphrey Art Director: Vernon Boes Print Buyer: Karen Hunt Production Service: Matrix Productions Inc. Copy Editor: Betty Duncan Cover Designer: Erik Adigard, Patricia McShane Cover Image: Erik Adigard Cover Printer: TK Compositor: International Typesetting and Composition Printer: TK © 2008, 2002 Duxbury, an imprint of Thomson Brooks/Cole, a part of The Thomson Corporation. Thomson, the Star logo, and Brooks/Cole are trademarks used herein under license. Thomson Higher Education 10 Davis Drive Belmont, CA 94002-3098 USA ALL RIGHTS RESERVED. No part of this work covered by the copyright hereon may be reproduced or used in any form or by any means—graphic, electronic, or mechanical, including photocopying, recording, taping, web distribution, information storage and retrieval systems, or in any other manner—without the written permission of the publisher. For more information about our products, contact us at: Thomson Learning Academic Resource Center 1-800-423-0563 For permission to use material from this text or product, submit a request online at http://www.thomsonrights.com. Any additional questions about permissions can be submitted by e-mail to
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