9780387979748

Probability

by
  • ISBN13:

    9780387979748

  • ISBN10:

    0387979743

  • Format: Hardcover
  • Copyright: 4/1/1993
  • Publisher: Springer Verlag

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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

Prefacep. V
Introductionp. 1
Equally Likely Outcomesp. 2
Interpretationsp. 11
Distributionsp. 19
Conditional Probability and Independencep. 33
Bayes' Rulep. 47
Sequences of Eventsp. 56
Summaryp. 73
Review Exercisesp. 74
Repeated Trials and Samplingp. 79
The Binomial Distributionp. 80
Normal Approximation: Methodp. 93
Normal Approximation: Derivation (Optional)p. 111
Poisson Approximationp. 117
Random Samplingp. 123
Summaryp. 130
Review Exercisesp. 132
Random Variablesp. 139
Introductionp. 139
Expectationp. 162
Standard Deviation and Normal Approximationp. 185
Discrete Distributionsp. 208
The Poisson Distributionp. 222
Symmetry (Optional)p. 237
Summaryp. 248
Review Exercisesp. 250
Continuous Distributionsp. 259
Probability Densitiesp. 260
Exponential and Gamma Distributionsp. 278
Hazard Rates (Optional)p. 296
Change of Variablep. 302
Cumulative Distribution Functionsp. 311
Order Statistics (Optional)p. 325
Summaryp. 334
Review Exercisesp. 336
Continuous Joint Distributionsp. 339
Uniform Distributionsp. 340
Densitiesp. 346
Independent Normal Variablesp. 357
Operations (Optional)p. 371
Summaryp. 386
Review Exercisesp. 387
Dependencep. 393
Conditional Distributions: Discrete Casep. 393
Conditional Expectation: Discrete Casep. 401
Conditioning: Density Casep. 410
Covariance and Correlationp. 430
Bivariate Normalp. 449
Summaryp. 464
Review Exercisesp. 466
Distribution Summariesp. 475
Discretep. 476
Continuousp. 477
Betap. 478
Binomialp. 479
Exponentialp. 480
Gammap. 481
Geometric and Negative Binomialp. 482
Hypergeometricp. 483
Normalp. 484
Poissonp. 486
Uniformp. 487
Examinationsp. 489
Solutions to Examinationsp. 498
Appendicesp. 505
Countingp. 507
Sumsp. 515
Calculusp. 517
Exponents and Logarithmsp. 525
Normal Tablep. 531
Brief Solutions to Odd-Numbered Exercisesp. 533
Indexp. 549
Table of Contents provided by Ingram. All Rights Reserved.

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