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First Course in Probability, A,9780131856622
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First Course in Probability, A

by
Edition:
8th
ISBN13:

9780131856622

ISBN10:
0131856626
Format:
Hardcover
Pub. Date:
1/1/2010
Publisher(s):
Prentice Hall
List Price: $132.00
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Summary

This introduction presents the mathematical theory of probability for readers in the fields of engineering and the sciences who possess knowledge of elementary calculus.Presents new examples and exercises throughout. Offers a new section that presents an elegant way of computing the moments of random variables defined as the number of events that occur. Gives applications to binomial, hypergeometric, and negative hypergeometric random variables, as well as random variables resulting from coupon collecting and match models. Provides additional results on inclusion-exclusion identity, Poisson paradigm, multinomial distribution, and bivariate normal distributionA useful reference for engineering and science professionals.

Table of Contents

Preface vii
Combinatorial Analysis
1(23)
Introduction
1(1)
The Basic Principle of Counting
2(1)
Permutations
3(3)
Combinations
6(4)
Multinomial Coefficients
10(2)
The Number of Integer Solutions of Equations*
12(12)
Summary
15(1)
Problems
16(3)
Theoretical Exercises
19(3)
Self-Test Problems and Exercises
22(2)
Axioms of Probability
24(42)
Introduction
24(1)
Sample Space and Events
24(5)
Axioms of Probability
29(2)
Some Simple Propositions
31(6)
Sample Spaces Having Equally Likely Outcomes
37(12)
Probability as a Continuous Set Function*
49(4)
Probability as a Measure of Belief
53(13)
Summary
54(1)
Problems
55(6)
Theoretical Exercises
61(2)
Self-Test Problems and Exercises
63(3)
Conditional Probability and Independence
66(66)
Introduction
66(1)
Conditional Probabilities
66(6)
Bayes' Formula
72(15)
Independent Events
87(14)
P(.|F) Is a Probability
101(31)
Summary
110(1)
Problems
111(13)
Theoretical Exercises
124(4)
Self-Test Problems and Exercises
128(4)
Random Variables
132(73)
Random Variables
132(6)
Discrete Random Variables
138(2)
Expected Value
140(4)
Expectation of a Function of a Random Variable
144(4)
Variance
148(2)
The Bernoulli and Binomial Random Variables
150(10)
Properties of Binomial Random Variables
155(3)
Computing the Binomial Distribution Function
158(2)
The Poisson Random Variable
160(13)
Computing the Poisson Distribution Function
173(1)
Other Discrete Probability Distributions
173(10)
The Geometric Random Variable
173(2)
The Negative Binomial Random Variable
175(3)
The Hypergeometric Random Variable
178(4)
The Zeta (or Zipf) Distribution
182(1)
Properties of the Cumulative Distribution Function
183(22)
Summary
185(2)
Problems
187(10)
Theoretical Exercises
197(4)
Self-Test Problems and Exercises
201(4)
Continuous Random Variables
205(53)
Introduction
205(4)
Expectation and Variance of Continuous Random Variables
209(5)
The Uniform Random Variable
214(4)
Normal Random Variables
218(12)
The Normal Approximation to the Binomial Distribution
225(5)
Exponential Random Variables
230(7)
Hazard Rate Functions
234(3)
Other Continuous Distributions
237(5)
The Gamma Distribution
237(2)
The Weibull Distribution
239(1)
The Cauchy Distribution
239(1)
The Beta Distribution
240(2)
The Distribution of a Function of a Random Variable
242(16)
Summary
244(3)
Problems
247(4)
Theoretical Exercises
251(3)
Self-Test Problems and Exercises
254(4)
Jointly Distributed Random Variables
258(69)
Joint Distribution Functions
258(9)
Independent Random Variables
267(13)
Sums of Independent Random Variables
280(8)
Conditional Distributions: Discrete Case
288(3)
Conditional Distributions: Continuous Case
291(5)
Order Statistics*
296(4)
Joint Probability Distribution of Functions of Random Variables
300(8)
Exchangeable Random Variables*
308(19)
Summary
311(2)
Problems
313(6)
Theoretical Exercises
319(4)
Self-Test Problems and Exercises
323(4)
Properties of Expectation
327(103)
Introduction
327(1)
Expectation of Sums of Random Variables
328(19)
Obtaining Bounds from Expectations via the Probabilistic Method*
342(2)
The Maximum-Minimums Identity*
344(3)
Moments of the Number of Events that Occur
347(8)
Covariance, Variance of Sums, and Correlations
355(10)
Conditional Expectation
365(17)
Definitions
365(2)
Computing Expectations by Conditioning
367(9)
Computing Probabilities by Conditioning
376(4)
Conditional Variance
380(2)
Conditional Expectation and Prediction
382(5)
Moment Generating Functions
387(12)
Joint Moment Generating Functions
397(2)
Additional Properties of Normal Random Variables
399(5)
The Multivariate Normal Distribution
399(3)
The Joint Distribution of the Sample Mean and Sample Variance
402(2)
General Definition of Expectation
404(26)
Summary
405(3)
Problems
408(10)
Theoretical Exercises
418(8)
Self-Test Problems and Exercises
426(4)
Limit Theorems
430(33)
Introduction
430(1)
Chebyshev's Inequality and the Weak Law of Large Numbers
430(4)
The Central Limit Theorem
434(9)
The Strong Law of Large Numbers
443(2)
Other Inequalities
445(9)
Bounding The Error Probability
454(9)
Summary
456(1)
Problems
457(2)
Theoretical Exercises
459(2)
Self-Test Problems and Exercises
461(2)
Additional Topics in Probability
463(24)
The Poisson Process
463(3)
Markov Chains
466(6)
Surprise, Uncertainty, and Entropy
472(4)
Coding Theory and Entropy
476(11)
Summary
483(1)
Theoretical Exercises
484(1)
Self-Test Problems and Exercises
485(2)
Simulation
487(74)
Introduction
487(3)
General Techniques for Simulating Continuous Random Variables
490(7)
The Inverse Transformation Method
490(1)
The Rejection Method
491(6)
Simulating from Discrete Distributions
497(2)
Variance Reduction Techniques
499(9)
Use of Antithetic Variables
500(1)
Variance Reduction by Conditioning
501(2)
Control Variates
503(1)
Summary
503(1)
Problems
504(2)
Self-Test Problems and Exercises
506(2)
APPENDICES
A Answers to Selected Problems
508(3)
B Solutions to Self-Test Problems and Exercises
511(50)
Index 561


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