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Introduction to Probability with Mathematica, Second Edition

ISBN: 9781420079388 | 1420079387
Edition: 2nd
Format: Hardcover
Publisher: Chapman & Hall/
Pub. Date: 9/21/2009

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SummaryTable of Contents
Introduction to Probability with Mathematica ® , Second Edition updates all exercises to the current version of Mathematica ® 6.0. The accompanying CD-ROM has also been updated to reflect changes in the latest version. This edition includes a new chapter dedicated to the treatment of stochastic processes and applications. It also expands coverage of probabilistic problems, multivariate random variables, distributions, and results about multivariate normal random variables, in particular with regard to quadratic forms. The text also adds new c... MORE
Discrete Probability
The Cast of Charactersp. 1
Properties of Probabilityp. 10
Simulationp. 23
Random Samplingp. 33
Sampling in Sequence without Replacementp. 34
Sampling in a Batch without Replacementp. 38
Other Sampling Situationsp. 42
Conditional Probabilityp. 48
Multiplication Rulesp. 51... MORE
Bayes' Formulap. 56
Independencep. 62
Discrete Distributions
Discrete Random Variables, Distributions, and Expectationsp. 73
Mean, Variance, and Other Momentsp. 79
Two Special Distributionsp. 85
Bernoulli and Binomial Random Variablesp. 94
Multinomial Distributionp. 102
Geometric and Negative Binomial Random Variablesp. 107
Poisson Distributionp. 115
Poisson Processesp. 120
Joint, Marginal, and Conditional Distributionsp. 124
More on Expectationp. 136
Covariance and Correlationp. 140
Conditional Expectationp. 148
Continuous Probability
From the Finite to the (Very) Infinitep. 159
Continuous Random Variables and Distributionsp. 171
Joint, Marginal, and Conditional Distributionsp. 178
Continuous Expectationp. 192
Continuous Distributions
The Normal Distributionp. 207
Bivariate Normal Distributionp. 225
Bivariate Normal Densityp. 229
Marginal and Conditional Distributionsp. 235
New Random Variables from Oldp. 246
C.D.F. Technique and Simulationp. 247
Moment-Generating Functionsp. 252
Order Statisticsp. 259
Gamma Distributionsp. 273
Main Propertiesp. 273
The Exponential Distributionp. 277
Chi-Square, Student's t, and F-Distributionsp. 281
Chi-Square Distributionp. 282
Student's t-Distributionp. 289
F-Distributionp. 293
Transformations of Normal Random Variablesp. 300
Linear Transformationsp. 301
Quadratic Forms in Normal Random Vectorsp. 306
Asymptotic Theory
Strong and Weak Laws of Large Numbersp. 313
Central Limit Theoremp. 320
Stochastic Processes and Applications
Markov Chainsp. 329
Short Run Distributionsp. 331
Long Run Distributionsp. 334
Absorbing Chainsp. 338
Poisson Processesp. 344
Queuesp. 352
Long Run Distribution of System Sizep. 353
Waiting Time Distributionp. 358
Simulating Queuesp. 359
Brownian Motionp. 365
Geometric Brownian Motionp. 373
Financial Mathematicsp. 379
Optimal Portfoliosp. 380
Option Pricingp. 385
Appendices
Introduction to Mathematicap. 395
Glossary of Mathematica Commands for Probabilityp. 423
Short Answers to Selected Exercisesp. 431
Referencesp. 445
Indexp. 447
Table of Contents provided by Ingram. All Rights Reserved.


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