Probability

by Pitman, Jim

• ISBN13: 9780387979748
• ISBN10: 0387979743
• Format: Hardcover
• Copyright: 1993-04-01
• Publisher: Springer Nature

Summary

This textbook is ideal for an undergraduate introduction to probability, with a calculus prerequisite. It is based on a course that the author has taught many times at Berkeley. The text's overall style is informal, but all results are stated precisely, and most are proved. Understanding is developed through intuitive explanations and examples. Graphs, diagrams, and geometrical ideals motivate results that might otherwise look likely purely formal manipulations.

Table of Contents

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
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