Probability and Random Variables

Lecture Notes

SES #	TOPICS
1	Permutations and Combinations (PDF)
2	Multinomial Coefficients and More Counting (PDF)
3	Sample Spaces and Set Theory (PDF)
4	Axioms of Probability (PDF)
5	Probability and Equal Likelihood (PDF)
6	Conditional Probabilities (PDF)
7	Bayes’ Formula and Independent Events (PDF)
8	Discrete Random Variables (PDF)
9	Expectations of Discrete Random Variables (PDF)
10	Variance (PDF)
11	Binomial Random Variables, Repeated Trials and the so-called Modern Portfolio Theory (PDF)
12	Poisson Random Variables (PDF)
13	Poisson Processes (PDF)
14	More Discrete Random Variables (PDF)
15	Continuous Random Variables (PDF)
16	Review for Midterm Exam 1 (PDF)
17	Midterm Exam 1 (No Lecture)
18	Uniform Random Variables (PDF)
19	Normal Random Variables (PDF)
20	Exponential Random Variables (PDF)
21	More Continuous Random Variables (PDF)
22	Joint Distribution Functions (PDF)
23	Sums of Independent Random Variables (PDF)
24	Expectation of Sums (PDF)
25	Covariance and Correlation (PDF)
26	Conditional Expectation (PDF)
27	Moment Generating Distributions (PDF)
28	Review for Midterm Exam 2 (PDF)
29	Midterm Exam 2 (No Lecture)
30	Weak Law of Large Numbers (PDF)
31	Central Limit Theorem (PDF)
32	Strong Law of Large Numbers and Jensen’s Inequality (PDF)
33	Markov Chains (PDF)
34	Entropy (PDF)
35	Martingales and the Optional Stopping Time Theorem (PDF)
36	Risk Neutral Probability and Black-Scholes (PDF)
37	Review for Final Exam (PDF)
38	Review for Final Exam (cont.) (PDF)
39	Review for Final Exam (cont.) (PDF)
40	Final Exam (No Lecture)