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Probability And Statistics for Computer Scientists


Edition: 1st
Author(s): Baron, Michael
ISBN10:  1584886412
ISBN13:  9781584886419
Format:  Hardcover
Pub. Date:  12/13/2006
Publisher(s): Chapman & Hall/

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Table of Contents
1 Introduction and Overview
1
1.1 Making decisions under uncertainty
1
1.2 Overview of this book
3
2 Probability
9
2.1 Sample space, events, and probability
9
2.2 Rules of Probability
11
2.3 Equally likely outcomes. Combinatorics
20
2.4 Conditional probability. Independence
28
3 Discrete Random Variables and their Distributions
41
3.1 Distribution of a random variable
41
3.2 Distribution of a random vector
46
3.3 Expectation and variance
49
3.4 Families of discrete distributions
61
4 Continuous Distributions
81
4.1 Probability density
81
4.2 Families of continuous distributions
86
4.3 Central Limit Theorem
100
5 Computer Simulations and Monte Carlo Methods
111
5.1 Introduction
111
5.2 Simulation of random variables
114
5.3 Solving problems by Monte Carlo methods
126
6 Stochastic Processes
143
6.1 Definitions and Classifications
143
6.2 Markov processes and Markov chains
145
6.3 Counting processes
162
6.4 Simulation of stochastic processes
172
7 Queuing Systems
183
7.1 Main components of a queuing system
183
7.2 The Little's Law
186
7.3 Bernoulli single-server queuing process
189
7.4 M/M/1 system
195
7.5 Multiserver queuing systems
202
7.6 Simulation of queuing systems
212
8 Introduction to Statistics
221
8.1 Population and sample, parameters and statistics
222
8.2 Simple descriptive statistics
224
8.3 Graphical statistics
238
9 Statistical Inference
253
9.1 Parameter estimation
253
9.2 Confidence intervals
262
9.3 Unknown standard deviation
270
9.4 Hypothesis testing
282
9.5 Bayesian estimation and hypothesis testing
305
10 Regression 327
10.1 Least squares estimation
327
10.2 Analysis of variance, prediction, and further inference
335
10.3 Multivariate regression
348
10.4 Model building
358
11 Appendix 371
11.1 Inventory of distributions
371
11.2 Distribution tables
377
11.3 Calculus review
391
11.4 Matrices and linear systems
398
11.5 Answers to selected exercises
404
Index 409

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