Probability : Springer Texts in Statistics - Jim Pitman

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Probability

By: Jim Pitman

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Hardcover | 12 May 1993 | Edition Number 1993

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Hardcover
560 Pages

Dimensions(cm)
21 x 23.7 x 3.7

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This is a text for a one-quarter or one-semester course in probability, aimed at students who have done a year of calculus. The book is organised so a student can learn the fundamental ideas of probability from the first three chapters without reliance on calculus. Later chapters develop these ideas further using calculus tools. The book contains more than the usual number of examples worked out in detail.
The most valuable thing for students to learn from a course like this is how to pick up a probability problem in a new setting and relate it to the standard body of theory. The more they see this happen in class, and the more they do it themselves in exercises, the better. The style of the text is deliberately informal. My experience is that students learn more from intuitive explanations, diagrams, and examples than they do from theorems and proofs. So the emphasis is on problem solving rather than theory.

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Preface	p. V
Introduction	p. 1
Equally Likely Outcomes	p. 2
Interpretations	p. 11
Distributions	p. 19
Conditional Probability and Independence	p. 33
Bayes' Rule	p. 47
Sequences of Events	p. 56
Summary	p. 73
Review Exercises	p. 74
Repeated Trials and Sampling	p. 79
The Binomial Distribution	p. 80
Normal Approximation: Method	p. 93
Normal Approximation: Derivation (Optional)	p. 111
Poisson Approximation	p. 117
Random Sampling	p. 123
Summary	p. 130
Review Exercises	p. 132
Random Variables	p. 139
Introduction	p. 139
Expectation	p. 162
Standard Deviation and Normal Approximation	p. 185
Discrete Distributions	p. 208
The Poisson Distribution	p. 222
Symmetry (Optional)	p. 237
Summary	p. 248
Review Exercises	p. 250
Continuous Distributions	p. 259
Probability Densities	p. 260
Exponential and Gamma Distributions	p. 278
Hazard Rates (Optional)	p. 296
Change of Variable	p. 302
Cumulative Distribution Functions	p. 311
Order Statistics (Optional)	p. 325
Summary	p. 334
Review Exercises	p. 336
Continuous Joint Distributions	p. 339
Uniform Distributions	p. 340
Densities	p. 346
Independent Normal Variables	p. 357
Operations (Optional)	p. 371
Summary	p. 386
Review Exercises	p. 387
Dependence	p. 393
Conditional Distributions: Discrete Case	p. 393
Conditional Expectation: Discrete Case	p. 401
Conditioning: Density Case	p. 410
Covariance and Correlation	p. 430
Bivariate Normal	p. 449
Summary	p. 464
Review Exercises	p. 466
Distribution Summaries	p. 475
Discrete	p. 476
Continuous	p. 477
Beta	p. 478
Binomial	p. 479
Exponential	p. 480
Gamma	p. 481
Geometric and Negative Binomial	p. 482
Hypergeometric	p. 483
Normal	p. 484
Poisson	p. 486
Uniform	p. 487
Examinations	p. 489
Solutions to Examinations	p. 498
Appendices	p. 505
Counting	p. 507
Sums	p. 515
Calculus	p. 517
Exponents and Logarithms	p. 525
Normal Table	p. 531
Brief Solutions to Odd-Numbered Exercises	p. 533
Index	p. 549
Table of Contents provided by Ingram. All Rights Reserved.

Probability

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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