Table of Contents

1. What is statistics and what is probability?
2. Discrete probability spaces
3. Examples of discrete probability spaces
4. Countable and uncountable
5. On infinite sums
6. Basic rules of probability
7. Inclusion-exclusion formula
8. Bonferroni's inequalities
9. Independence - a first look
10. Conditional probability and independence
11. Independence of three or more events
12. Subtleties of conditional probability
13. Discrete probability distributions
14. General probability distributions
15. Uncountable probability spaces - conceptual difficulties
16. Examples of continuous distributions
17. Simulation
18. Joint distributions
19. Change of variable formula
20. Independence and conditioning of random variables
21. Mean and Variance
22. Makov's and Chebyshev's inequalities
23. Weak law of large numbers
24. Monte-Carlo integration
25. Central limit theorem
26. Poisson limit for rare events
27. Entropy, Gibbs distribution
28. Introduction
29. Estimation problems
30. Properties of estimates
31. Confidence intervals
32. Confidence interval for the mean
33. Actual confidence by simulation
34. Hypothesis testing - first examples
35. Testing for the mean of a normal population
36. Testing for the difference between means of two normal populations
37. Testing for the mean in absence of normality
38. Chi-squared test for goodness of fit
39. Tests for independence
40. Regression and Linear regression