Introduction to Probability and Its Applications

by Scheaffer, Richard L.

• ISBN13: 9780534237905
• ISBN10: 0534237908
• Edition: 2nd
• Format: Hardcover
• Copyright: 1994-11-18
• Publisher: Duxbury Press

Summary

Introduction to Probability and its Applications provides a solid and straightforward one-semester introduction to probability, focusing on the subject's utility in solving real-world problems. The text's hallmark applications-updated and greatly expanded in the Third Edition-illuminate the diverse ways in which probability affects our lives. Numerous examples and exercises using current data provide practice for students in calculating probabilities in a variety of settings. An accessible presentation gives students of varying academic backgrounds a thorough understanding of the underlying theory and an intuitive sense o flow to apply probability concepts in the real world. The text provides a solid background for students going on to more advanced courses in probability and statistics, while also providing a working knowledge of probability for those who must apply it in future courses or careers in engineering and the sciences.

Table of Contents

Probability in the World Around Us	1	(5)
Why Study Probability?	1	(1)
Deterministic and Probabilistic Models	2	(1)
Applications of Probability	3	(2)
A Brief Historical Note	5	(1)
A Look Ahead	5	(1)
Probability	6	(61)
Understanding Randomness: An Intuitive Notion of Probability	6	(3)
A Brief Review of Set Notation	9	(4)
Definition of Probability	13	(8)
Counting Rules Useful in Probability	21	(11)
Conditional Probability and Independence	32	(8)
Rules of Probability	40	(17)
Odds, Odds Ratios, and Relative Risk	57	(3)
Activities for Students: Simulation	60	(2)
Summary	62	(5)
Supplementary Exercises	62	(5)
Discrete Probability-Distributions	67	(71)
Random Variables and Their Probability Distributions	67	(6)
Expected Values of Random Variables	73	(13)
The Bernoulli Distribution	86	(1)
The Binomial Distribution	87	(10)
The Geometric Distribution	97	(3)
The Negative Binomial Distribution	100	(4)
The Poisson Distribution	104	(5)
The Hypergeometric Distribution	109	(6)
The Moment-Generating Function	115	(2)
The Probability-generating Function	117	(3)
Markov Chains	120	(8)
Activities for Students: Simulation	128	(5)
Summary	133	(5)
Supplementary Exercises	134	(4)
Continuous Probability Distributions	138	(85)
Continuous Random Variables and Their Probability Distributions	138	(8)
Expected Values of Continuous Random Variables	146	(5)
The Uniform Distribution	151	(5)
The Exponential Distribution	156	(6)
The Gamma Distribution	162	(5)
The Normal Distribution	167	(21)
The Beta Distribution	188	(4)
The Weibull Distribution	192	(6)
Reliability	198	(4)
Moment-generating Functions for Continuous Random Variables	202	(4)
Expectations of Discontinuous Functions and Mixed Probability Distributions	206	(5)
Activities for Students: Simulation	211	(7)
Summary	218	(5)
Supplementary Exercises	218	(5)
Multivariate Probability Distributions	223	(46)
Bivariate and Marginal Probability Distributions	223	(9)
Conditional Probability Distributions	232	(3)
Independent Random Variables	235	(4)
Expected Values of Functions of Random Variables	239	(11)
The Multinomial Distribution	250	(5)
More on the Moment-generating Function	255	(2)
Conditional Expectations	257	(4)
Compounding and Its Applications	261	(1)
Summary	262	(7)
Supplementary Exercises	263	(6)
Functions of Random Variables	269	(33)
Introduction	269	(1)
Method of Distribution Functions	270	(6)
Method of Transformations	276	(5)
Method of Conditioning	281	(2)
Method of Moment-generating Functions	283	(6)
Order Statistics	289	(6)
Probability-generating Functions: Applications to Random Sums of Random Variables	295	(3)
Summary	298	(4)
Supplementary Exercises	298	(4)
Some Approximations to Probability Distributions: Limit Theorems	302	(25)
Introduction	302	(1)
Convergence in Probability	302	(4)
Convergence in Distribution	306	(5)
The Central Limit Theorem	311	(13)
Combination of Convergence in Probability and Convergence in Distribution	324	(1)
Summary	325	(2)
Supplementary Exercises	325	(2)
Extended Applications of Probability	327	(15)
The Poisson Process	327	(3)
Birth and Death Processes: Biological Applications	330	(2)
Queues: Engineering Applications	332	(1)
Arrival Times for the Poisson Process	333	(1)
Infinite Server Queue	334	(2)
Renewal Theory: Reliability Applications	336	(3)
Summary	339	(3)
Exercises	340	(2)
Appendix Tables	342	(11)
Notes on Computer Simulations	353	(2)
References	355	(2)
Answers to Selected Exercises	357	(16)
Index	373