Outline
1. 1 Modelling discrete and continuous quantities
2. 2 Cumulative distribution functions
3. 3 Independence
4. 4 Families of discrete probability distributions
5. 5 Families of continuous probability distributions
6. 1 The expected value
7. 2 Raw and central moments / the variance
8. 3 Skewness and excess kurtosis
9. 4 Chebyshev’s Inequality
10. 5 Jensen’s Inequality
11. 1 The moment generating function
12. 2 Linear transformations and sums
13. 3 Distribution of the maximum and minimum
14. 1 Cumulants
15. 2 Cumulants of sums
16. 3 The Central Limit Theorem
17. 4 Approximating distributions via the CLT
18. 5 Proof of the CLT
19. 1 Transformations of random variables
20. 2 Simulation using the inverse transform method
21. 1 Discrete random variables
22. 2 Continuous random variables
23. 3 Independence
24. Expectations of functions
25. 1 Conditional probability functions
26. 2 Conditional densities
27. 3 Conditional expectation
28. 4 Conditional variance
29. COVARIANCE AND CORRELATION
30. 1 The tower law of conditional expectations
31. 2 Conditional and unconditional variance
32. 3 Conditioning functions of X and Y
33. 1 Compound random variables
34. 2 Generating functions of compound random variables