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First Course in Probability, A

ISBN: 9780130338518 | 0130338516
Edition: 6th
Format: Hardcover
Publisher: PRENTICE HALL
Pub. Date: 1/1/2002

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SummaryTable of Contents
For upper level or undergraduate/graduate level introduction to probability for math, science, engineering, and business students with a background in elementary calculus. This market-leading introduction to probability features exceptionally clear explanations of the mathematics of probability theory and explores its many diverse applications through numerous interesting and motivational examples. The outstanding problem sets and intuitive explanations are hallmark features of this market leading text.
Prefacevi
Combinatorial Analysis
1(23)
Introduction
1(1)
... MORE
The Basic Principle of Counting
2(1)
Permutations
3(2)
Combinations
5(5)
Multinomial Coefficients
10(2)
The Number of Integer Solutions of Equations*
12(12)
Summary
15(1)
Problems
15(7)
Theoretical Exercises
22(1)
Self-Test Problems and Exercises
22(2)
Axioms of Probability
24(40)
Introduction
24(1)
Sample Space and Events
24(4)
Axioms of Probability
28(3)
Some Simple Propositions
31(4)
Sample Spaces Having Equally Likely Outcomes
35(12)
Probability As a Continuous Set Function*
47(4)
Probability As a Measure of Belief
51(13)
Summary
52(1)
Problems
53(6)
Theoretical Exercises
59(2)
Self-Test Problems and Exercises
61(3)
Conditional Probability and Independence
64(58)
Introduction
64(1)
Conditional Probabilities
64(5)
Bayes' Formula
69(14)
Independent Events
83(13)
P(•/F) is a Probability*
96(26)
Summary
103(1)
Problems
104(11)
Theoretical Exercises
115(4)
Self-Test Problems and Exercises
119(3)
Random Variables
122(65)
Random Variables
122(5)
Discrete Random Variables
127(3)
Expected Value
130(3)
Expectation of a Function of a Random Variable
133(4)
Variance
137(2)
The Bernoulli and Binomial Random Variables
139(10)
Properties of Binomial Random Variables
144(3)
Computing the Binomial Distribution Function
147(2)
The Poisson Random Variable
149(9)
Computing the Poisson Distribution Function
157(1)
Other Discrete Probability Distribution
158(8)
The Geometric Random Variable
158(2)
The Negative Binomial Random Variable
160(2)
The Hypergeometric Random Variable
162(4)
The Zeta (or Zipf) distribution
166(1)
Properties of the Cumulative Distribution Function
166(21)
Summary
169(2)
Problems
171(9)
Theoretical Exercises
180(4)
Self-Test Problems and Exercises
184(3)
Continuous Random Variables
187(52)
Introduction
187(3)
Expectation and Variance of Continuous Random Variables
190(5)
The Uniform Random Variable
195(4)
Normal Random Variables
199(11)
The Normal Approximation to the Binomial Distribution
206(4)
Exponential Random Variables
210(7)
Hazard Rate Functions
215(2)
Other Continuous Distributions
217(6)
The Gamma Distribution
217(3)
The Weibull Distribution
220(1)
The Cauchy Distribution
220(1)
The Beta Distribution
221(2)
The Distribution of a Function of a Random Variable
223(16)
Summary
225(3)
Problems
228(4)
Theoretical Exercises
232(3)
Self-Test Problems and Exercises
235(4)
Jointly Distributed Random Variables
239(65)
Joint Distribution Functions
239(9)
Independent Random Variables
248(12)
Sums of Independent Random Variables
260(8)
Conditional Distributions: Discrete Case
268(2)
Conditional Distributions: Continuous Case
270(3)
Order Statistics*
273(4)
Joint Probability Distribution of Functions of Random Variables
277(8)
Exchangeable Random Variables*
285(19)
Summary
288(2)
Problems
290(6)
Theoretical Exercises
296(3)
Self-Test Problems and Exercises
299(5)
Properties of Expectations
304(96)
Introduction
304(1)
Expectation of Sums of Random Variables
305(22)
Obtaining Bounds from Expectations via the Probabilistic Method*
321(3)
The Maximum-Minimums Identity*
324(3)
Covariance, Variance of Sums, and Correlations
327(13)
Conditional Expectation
340(16)
Definitions
340(3)
Computing Expectations by Conditioning
343(7)
Computing Probabilities by Conditioning
350(4)
Conditional Variance
354(2)
Conditional Expectation and Prediction
356(5)
Moment Generating Functions
361(12)
Joint Moment Generating Functions
371(2)
Additional Properties of Normal Random Variables
373(2)
The Multivariate Normal Distribution
373(1)
The Joint Distribution of the Sample Mean and Sample Variance
374(1)
General Definition of Expectation*
375(25)
Summary
377(2)
Problems
379(10)
Theoretical Exercises
389(8)
Self-Test Problems and Exercises
397(3)
Limit Theorems
400(32)
Introduction
400(1)
Chebyshev's Inequality and the Weak Law of Large Numbers
400(3)
The Central Limit Theorem
403(9)
The Strong Law of Large Numbers
412(5)
Other Inequalities
417(7)
Bounding the Error Probability When Approximating a Sum of Independent Bernoulli Random Variables by a Poisson
424(8)
Summary
426(1)
Problems
427(2)
Theoretical Exercises
429(1)
Self-Test Problems and Exercises
430(2)
Additional Topics in Probability
432(23)
The Poisson Process
432(3)
Markov Chains
435(5)
Surprise, Uncertainty, and Entropy
440(5)
Coding Theory and Entropy
445(10)
Summary
451(1)
Theoretical Exercises and Problems
452(2)
Self-Test Problems and Exercises
454(1)
References
454(1)
Simulation
455(20)
Introduction
455(3)
General Techniques for Simulating Continuous Random Variables
458(7)
The Inverse Transformation Method
458(1)
The Rejection Method
459(6)
Simulating from Discrete Distributions
465(2)
Variance Reduction Techniques
467(8)
Use of Antithetic Variables
468(1)
Variance Reduction by Conditioning
468(2)
Control Variates
470(1)
Summary
471(1)
Problems
471(3)
Self-Test Problems and Exercises
474(1)
References
474(1)
Appendix A Answers to Selected Problems475(3)
Appendix B Solutions to Self-Test Problems and Exercises478(41)
Index519

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