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Introduction To Probability With Mathematica Book

Introduction To Probability With Mathematica
Introduction To Probability With Mathematica, , Introduction To Probability With Mathematica has a rating of 3 stars
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  • Introduction To Probability With Mathematica
  • Written by author Kevin J. Hastings
  • Published by CRC Press, January 2001
  • Newcomers to the world of probability face several potential stumbling blocks. They often struggle with key concepts-sample space, random variable, distribution, and expectation; they must regularly confront integration, infrequently mastered in calculus
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Chapter 1Discrete Probability
1.1The Cast of Characters1
1.2Properties of Probability10
1.3Simulation25
1.4Random Sampling38
Sampling in Sequence without Replacement38
Sampling in a Batch without Replacement42
Other Sampling Situations48
1.5Conditional Probability54
Multiplication Rules56
Bayes' Formula61
1.6Independence67
Chapter 2Discrete Distributions
2.1Discrete Random Variables, Distributions, and Expectations79
Mean, Variance, and Other Moments86
Two Special Distributions91
2.2Bernoulli and Binomial Random Variables101
2.3Geometric and Negative Binomial Random Variables110
2.4Poisson Distribution119
Poisson Processes124
2.5Joint, Marginal, and Conditional Distributions129
2.6More on Expectation146
Chapter 3Continuous Probability
3.1From the Finite to the (Very) Infinite163
3.2Continuous Random Variables and Distributions171
Joint, Marginal, and Conditional Distributions179
3.3Continuous Expectation194
Chapter 4Continuous Distributions
4.1The Normal Distribution209
4.2Bivariate Normal Distribution225
Bivariate Normal Density227
Marginal and Conditional Distributions233
4.3New Random Variables from Old245
C.D.F. Technique and Simulation246
Moment-Generating Functions252
4.4Gamma Distributions259
Main Properties259
The Exponential Distribution264
More on the Poisson Process267
4.5Chi-Square, Student's t, and F-distributions272
Chi-Square Distribution272
Student's t-Distribution279
F-Distribution283
Chapter 5Asymptotic Theory
5.1Strong and Weak Laws of Large Numbers293
5.2Central Limit Theorem301
Chapter 6Applications of Probability
6.1Markov Chains309
6.2Queues320
Long-Run Distribution of System Size322
Waiting Time Distribution327
Simulating Queues328
6.3Mathematical Finance336
Optimal Portfolios336
Option Pricing341
Appendix
A.Short Answers to Selected Exercises353
B.Glossary of Mathematica Commands for Probability365
References373
Index375


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