I Randomness
1. Outcomes, Events, and Sample Spaces
2. Probability
3. Independent Events
4. Conditional Probability
5. Bayes' Theorem
II Discrete Random Variables
6. Random Variables; Discrete Versus Continuous
7. Probability Mass Functions and Cumulative Distribution Functions
8. Jointly Distributed Random Variables; Independence and Conditioning
9. Expected Values of Discrete Random Variables
10. Expected Values of Sums of Random Variables
11. Expected Values of Functions of Discrete Random Variables; Variance of Discrete Random Variables
12. Summary and Review of Discrete Random Variables
III Named Discrete Random Variables
13. Bernoulli Random Variables
14. Binomial Random Variables
15. Geometric Random Variables
16. Negative Binomial Random Variables
17. Poisson Random Variables
18. Hypergeometric Random Variables
19. Discrete Uniform Random Variables
20. Summary and Review of Named Discrete Random Variables
IV Counting
21. Introduction to Counting
22. Two Case Studies in Counting
V Continuous Random Variables
23. Continuous Random Variables; Probability Density Functions
24. Joint Densities
25. Independent Continuous Random Variables
26. Conditional Distributions for Continuous Random Variables
27. Expected Values of Continuous Random Variables
28. Expected Values of Functions of Continuous Random Variables; Variance of Continuous Random Variables
29. Summary and Review of Continuous Random Variables
VI Named Continuous Random Variables
30. Continuous Uniform Random Variables
31. Exponential Random Variables
32. Gamma Random Variables
33. Beta Random Variables
34. Normal Random Variables
35. Sums of Independent Normal Random Variables
36. Central Limit Theorem
37. Summary and Review of Named Continuous Random Variables
VII Additional Topics
38. Variance of Sums of Random Variables; Covariance; Correlation
39. Conditional Expectation
40. Markov and Chebyshev Inequalities
41. Order Statistics
42. Moment Generating Functions
43. Transformations of One or Two Random Variables
44. Review Questions for All Chapters