An Introduction to Probability Theory and Its Applications, Volume 2 [Paperback]

The classic text for understanding complex statistical probability

An Introduction to Probability Theory and Its Applications offers comprehensive explanations to complex statistical problems. Delving deep into densities and distributions while relating critical formulas, processes and approaches, this rigorous text provides a solid grounding in probability with practice problems throughout. Heavy on application without sacrificing theory, the discussion takes the time to explain difficult topics and how to use them. This new second edition includes new material related to the substitution of probabilistic arguments for combinatorial artifices as well as new sections on branching processes, Markov chains, and the DeMoivre-Laplace theorem.

1. Introduction

2. Densities. Convolutions

3. The Exponential Density

4. Waiting Time Paradoxes. The Poisson Process

5. The Persistence of Bad Luck

6. Waiting Times and Order Statistics

7. The Uniform Distribution

8. Random Splittings

9. Convolutions and Covering Theorems

10. Random Directions

11. The Use of Lebesgue Measure

12. Empirical Distributions

13. Problems for Solution

Chapter II Special Densities. Randomization

1. Notations and Conventions

2. Gamma Distributions

3. Related Distributions of Statistics

4. Some Common Densities

5. Randomization and Mixtures

6. Discrete Distributions

7. Bessel Functions and Random Walks

8. Distributions on a Circle

9. Problems for Solution