Introduction To Probability

by Bertsekas, Dimitri P.; Tsitsiklis, John N.

• ISBN13: 9781886529403
• ISBN10: 188652940X
• Format: Hardcover
• Copyright: 2002-06-30
• Publisher: Athena Scientific

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