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E-raamat: Introduction to Probability with Mathematica

(Knox College, Galesburg, Illinois, USA)
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 21-Sep-2009
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781040171141
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Introduction to Probability with MathematicaSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 21-Sep-2009
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781040171141
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Hastings (Knox College, Illinois) offers a textbook designed to provide students with a solid knowledge of the main concepts in probability that they will need in such fields as statistics, operations research, and finance. They include event, sample space, random variable, distribution, and expectation. Another goal is to encourage good writing. Finding simulation to be a powerful pedagogical tool, he tailors the course to the popular mathematics software package, where simulation is easy. No date is noted for the first edition, but one of the reasons for this second is to account for the newest versions of Mathematica. The disk contains executable notebooks. Annotation ©2009 Book News, Inc., Portland, OR (booknews.com)

Updated to conform to Mathematica® 7.0, Introduction to Probability with Mathematica®, Second Edition continues to show students how to easily create simulations from templates and solve problems using Mathematica. It provides a real understanding of probabilistic modeling and the analysis of data and encourages the application of these ideas to practical problems. The accompanying CD-ROM offers instructors the option of creating class notes, demonstrations, and projects.

New to the Second Edition

  • Expanded section on Markov chains that includes a study of absorbing chains
  • New sections on order statistics, transformations of multivariate normal random variables, and Brownian motion
  • More example data of the normal distribution
  • More attention on conditional expectation, which has become significant in financial mathematics
  • Additional problems from Actuarial Exam P
  • New appendix that gives a basic introduction to Mathematica
  • New examples, exercises, and data sets, particularly on the bivariate normal distribution
  • New visualization and animation features from Mathematica 7.0
  • Updated Mathematica notebooks on the CD-ROM

After covering topics in discrete probability, the text presents a fairly standard treatment of common discrete distributions. It then transitions to continuous probability and continuous distributions, including normal, bivariate normal, gamma, and chi-square distributions. The author goes on to examine the history of probability, the laws of large numbers, and the central limit theorem. The final chapter explores stochastic processes and applications, ideal for students in operations research and finance.

Arvustused

If you own the first edition, you will be very pleased with the second edition. It is more complete, better organized, and even more well-presented. If you don't own the first edition, and are looking for an effective tool for conveying probabilistic concepts, Hastings' book should certainly be one you consider. -Jane L. Harvill, The American Statistician, November 2011 Introduction to Probability with Mathematica adds computational exercises to the traditional undergraduate probability curriculum without cutting out theory. ... a good textbook for a class with a strong emphasis on hands-on experience with probability. ... One interesting feature of the book is that each set of exercises includes a few problems taken from actuarial exams. No doubt this will comfort students who are taking a probability course in hopes that it will prepare them for an actuarial exam. Another interesting feature is the discussion of the Central Limit Theorem. The book goes into an interesting discussion of the history of the theorem ... . -MAA Reviews, December 2009

Chapter 1 Discrete Probability
1.1 The Cast of Characters
1
1.2 Properties of Probability
10
1.3 Simulation
23
1.4 Random Sampling
33
Sampling in Sequence without Replacement
34
Sampling in a Batch without Replacement
38
Other Sampling Situations
42
1.5 Conditional Probability
48
Multiplication Rules
51
Bayes' Formula
56
1.6 Independence
62
Chapter 2 Discrete Distributions
2.1 Discrete Random Variables, Distributions, and Expectations
73
Mean, Variance, and Other Moments
79
Two Special Distributions
85
2.2 Bernoulli and Binomial Random Variables
94
Multinomial Distribution
102
2.3 Geometric and Negative Binomial Random Variables
107
2.4 Poisson Distribution
115
Poisson Processes
120
2.5 Joint, Marginal, and Conditional Distributions
124
2.6 More on Expectation
136
Covariance and Correlation
140
Conditional Expectation
148
Chapter 3 Continuous Probability
3.1 From the Finite to the (Very) Infinite
159
3.2 Continuous Random Variables and Distributions
171
Joint, Marginal, and Conditional Distributions
178
3.3 Continuous Expectation
192
Chapter 4 Continuous Distributions
4.1 The Normal Distribution
207
4.2 Bivariate Normal Distribution
225
Bivariate Normal Density
229
Marginal and Conditional Distributions
235
4.3 New Random Variables from Old
246
C.D.F. Technique and Simulation
247
Moment—Generating Functions
252
4.4 Order Statistics
259
4.5 Gamma Distributions
273
Main Properties
273
The Exponential Distribution
277
4.6 Chi—Square, Student's t, and F—Distributions
281
Chi—Square Distribution
282
Student's t—Distribution
289
F—Distribution
293
4.7 Transformations of Normal Random Variables
300
Linear Transformations
301
Quadratic Forms in Normal Random Vectors
306
Chapter 5 Asymptotic Theory
5.1 Strong and Weak Laws of Large Numbers
313
5.2 Central Limit Theorem
320
Chapter 6 Stochastic Processes and Applications
6.1 Markov Chains
329
Short Run Distributions
331
Long RIM Distributions
334
Absorbing Chains
338
6.2 Poisson Processes
344
6.3 Queues
352
Long Run Distribution of System Size
353
Waiting Time Distribution
358
Simulating Queues
359
6.4 Brownian Motion
365
Geometric Brownian Motion
373
6.5 Financial Mathematics
379
Optimal Portfolios
380
Option Pricing
385
Appendices
A. Introduction to Mathematica
395
B. Glossary of Mathematica Commands for Probability
423
C. Short Answers to Selected Exercises
431
References 445
Index 447
Kevin J. Hastings is a professor of mathematics at Knox College in Galesburg, Illinois.
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