Introduction To Probability,9781886529403

Introduction To Probability

by ;
ISBN13: 9781886529403
ISBN10: 188652940X
Format: Hardcover
Pub. Date: 2002-06-30
Publisher(s): Athena Scientific
List Price: $79.00

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Table of Contents

Sample Space and Probability
1(70)
Sets
3(3)
Probabilistic Models
6(12)
Conditional Probability
18(10)
Total Probability Theorem and Bayes' Rule
28(6)
Independence
34(9)
Counting
43(7)
Summary and Discussion
50(21)
Problems
52(19)
Discrete Random Variables
71(68)
Basic Concepts
72(2)
Probability Mass Functions
74(6)
Functions of Random Variables
80(1)
Expectation, Mean, and Variance
81(11)
Joint PMFs of Multiple Random Variables
92(6)
Conditioning
98(12)
Independence
110(6)
Summary and Discussion
116(23)
Problems
119(20)
General Random Variables
139(70)
Continuous Random Variables and PDFs
140(8)
Cumulative Distribution Functions
148(4)
Normal Random Variables
152(6)
Conditioning on an Event
158(6)
Multiple Continuous Random Variables
164(15)
Derived Distributions
179(11)
Summary and Discussion
190(19)
Problems
192(17)
Further Topics on Random Variables
209(62)
Transforms
210(11)
Sums of Independent Random Variables - Convolution
221(4)
More on Conditional Expectation and Variance
225(7)
Sum of a Random Number of Independent Random Variables
232(4)
Covariance and Correlation
236(4)
Least Squares Estimation
240(7)
The Bivariate Normal Distribution
247(8)
Summary and Discussion
255(16)
Problems
257(14)
The Bernoulli and Poisson Processes
271(42)
The Bernoulli Process
273(12)
The Poisson Process
285(14)
Summary and Discussion
299(14)
Problems
301(12)
Markov Chains
313(66)
Discrete-Time Markov Chains
314(7)
Classification of States
321(5)
Steady-State Behavior
326(11)
Absorption Probabilities and Expected Time to Absorption
337(7)
Continuous-Time Markov Chains
344(8)
Summary and Discussion
352(27)
Problems
354(25)
Limit Theorems
379(32)
Markov and Chebyshev Inequalities
381(2)
The Weak Law of Large Numbers
383(3)
Convergence in Probability
386(2)
The Central Limit Theorem
388(7)
The Strong Law of Large Numbers
395(2)
Summary and Discussion
397(14)
Problems
399(12)
Index 411

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