Introduction to Probability Theory : With Contemporary Applications

by Helms, Lester L.

• ISBN13: 9780716730231
• ISBN10: 0716730235
• Format: Hardcover
• Copyright: 1996-07-01
• Publisher: W. H. Freeman Company

Summary

This class-tested upper-level text presents probability theory clearly, using detailed written explanations whenever necessary to ensure that students understand the underlying principles. Emphasis is on mastering a coherent set of rules and developing problem-solving skills.

Table of Contents

Preface	ix
1 Classical Probability	1	(24)
1.1 Beginnings	1	(1)
1.2 Basic Rules	2	(3)
1.3 Counting	5	(7)
1.4 Equally Likely Case	12	(5)
1.5 Other Models	17	(8)
2 Axioms of Probability	25	(35)
2.1 Introduction	25	(1)
2.2 Set Theory	26	(5)
2.3 Countable Sets	31	(4)
2.4 Axioms	35	(6)
2.5 Properties of Probability Functions	41	(4)
2.6 Conditional Probability and Independence	45	(7)
2.7 Some Applications	52	(8)
3 Random Variables	60	(39)
3.1 Introduction	60	(1)
3.2 Random Variables	60	(12)
3.3 Independent Random Variables	72	(9)
3.4 Generating Functions	81	(11)
3.5 Gambler's Ruin Problem	92	(4)
3.6 Appendix	96	(3)
4 Expectation	99	(45)
4.1 Introduction	99	(1)
4.2 Expected Value	99	(8)
4.3 Properties of Expectation	107	(10)
4.4 Covariance and Correlation	117	(8)
4.5 Conditional Expectation	125	(8)
4.6 Entropy	133	(11)
5 Stochastic Processes	144	(37)
5.1 Introduction	144	(1)
5.2 Markov Chains	145	(14)
5.3 Random Walks	159	(8)
5.4 Branching Processes	167	(5)
5.5 Prediction Theory	172	(9)
6 Continuous Random Variables	181	(45)
6.1 Introduction	181	(1)
6.2 Random Variables	182	(8)
6.3 Distribution Functions	190	(9)
6.4 Joint Distribution Functions	199	(10)
6.5 Computations with Densities	209	(7)
6.6 Multivariate and Conditional Densities	216	(10)
7 Expectation Revisited	226	(41)
7.1 Introduction	226	(1)
7.2 Riemann-Stieltjes Integral	226	(8)
7.3 Expectation and Conditional Expectation	234	(9)
7.4 Normal Density	243	(12)
7.5 Covariance and Covariance Functions	255	(12)
8 Continuous Parameter Markov Processes	267	(33)
8.1 Introduction	267	(1)
8.2 Poisson Process	267	(6)
8.3 Birth and Death Processes	273	(5)
8.4 Markov Chains	278	(7)
8.5 Matrix Calculus	285	(8)
8.6 Stationary Distributions	293	(7)
Solutions to Exercises	300	(46)
Standard Normal Distribution Function	346	(1)
Symbols	347	(1)
Index	348