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Introduction to Probability with Mathematica 2nd edition [Pehme köide]

(Knox College, Galesburg, Illinois, USA)
  • Formaat: Paperback / softback, 468 pages, kõrgus x laius: 234x156 mm, kaal: 453 g
  • Ilmumisaeg: 19-Sep-2019
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 0367385198
  • ISBN-13: 9780367385194
  • Formaat: Paperback / softback, 468 pages, kõrgus x laius: 234x156 mm, kaal: 453 g
  • Ilmumisaeg: 19-Sep-2019
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 0367385198
  • ISBN-13: 9780367385194
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 accompanyingdownloadable resources offer 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 downloadable resources.











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.
Chapter 1 Discrete Probability
1.1 The Cast of Characters
1(9)
1.2 Properties of Probability
10(13)
1.3 Simulation
23(10)
1.4 Random Sampling
33(15)
Sampling in Sequence without Replacement
34(4)
Sampling in a Batch without Replacement
38(4)
Other Sampling Situations
42(6)
1.5 Conditional Probability
48(14)
Multiplication Rules
51(5)
Bayes' Formula
56(6)
1.6 Independence
62(11)
Chapter 2 Discrete Distributions
2.1 Discrete Random Variables, Distributions, and Expectations
73(21)
Mean, Variance, and Other Moments
79(6)
Two Special Distributions
85(9)
2.2 Bernoulli and Binomial Random Variables
94(13)
Multinomial Distribution
102(5)
2.3 Geometric and Negative Binomial Random Variables
107(8)
2.4 Poisson Distribution
115(9)
Poisson Processes
120(4)
2.5 Joint, Marginal, and Conditional Distributions
124(12)
2.6 More on Expectation
136(23)
Covariance and Correlation
140(8)
Conditional Expectation
148(11)
Chapter 3 Continuous Probability
3.1 From the Finite to the (Very) Infinite
159(12)
3.2 Continuous Random Variables and Distributions
171(21)
Joint, Marginal, and Conditional Distributions
178(14)
3.3 Continuous Expectation
192(15)
Chapter 4 Continuous Distributions
4.1 The Normal Distribution
207(18)
4.2 Bivariate Normal Distribution
225(21)
Bivariate Normal Density
229(6)
Marginal and Conditional Distributions
235(11)
4.3 New Random Variables from Old
246(13)
C.D.F. Technique and Simulation
247(5)
Moment-Generating Functions
252(7)
4.4 Order Statistics
259(14)
4.5 Gamma Distributions
273(8)
Main Properties
273(4)
The Exponential Distribution
277(4)
4.6 Chi-Square, Student's t, and F-Distributions
281(19)
Chi-Square Distribution
282(7)
Student's Distribution
289(4)
F-Distribution
293(7)
4.7 Transformations of Normal Random Variables
300(13)
Linear Transformations
301(5)
Quadratic Forms in Normal Random Vectors
306(7)
Chapter 5 Asymptotic Theory
5.1 Strong and Weak Laws of Large Numbers
313(7)
5.2 Central Limit Theorem
320(9)
Chapter 6 Stochastic Processes and Applications
6.1 Markov Chains
329(15)
Short Run Distributions
331(3)
Long Run Distributions
334(4)
Absorbing Chains
338(6)
6.2 Poisson Processes
344(8)
6.3 Queues
352(13)
Long Run Distribution of System Size
353(5)
Waiting Time Distribution
358(1)
Simulating Queues
359(6)
6.4 Brownian Motion
365(14)
Geometric Brownian Motion
373(6)
6.5 Financial Mathematics
379(16)
Optimal Portfolios
380(5)
Option Pricing
385(10)
Appendices
A Introduction to Mathematica
395(28)
B Glossary of Mathematica Commands for Probability
423(8)
C Short Answers to Selected Exercises
431(14)
References 445(2)
Index 447
Kevin J. Hastings is a professor of mathematics at Knox College in Galesburg, Illinois.