| 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 | Review for midterm exam 1 (PDF) |
| 16 | Midterm exam 1 [no lecture notes] |
| 17 | Continuous random variables (PDF) |
| 18 | Normal random variables (PDF) |
| 19 | Exponential random variables (PDF) |
| 20 | More continuous random variables (PDF) |
| 21 | Joint distribution functions (PDF) |
| 22 | Sums of independent random variables (PDF) |
| 23 | Expectation of sums (PDF) |
| 24 | Covariance and some conditional expectation exercises (PDF) |
| 25 | Conditional expectation (PDF) |
| 26 | Moment generating functions (PDF) |
| 27 | Weak law of large numbers (PDF) |
| 28 | Review for midterm exam 2 (PDF) |
| 29 | Midterm exam 2 [no lecture notes] |
| 30 | Central limit theorem (PDF) |
| 31 | Strong law of large numbers and Jensen's inequality (PDF) |
| 32 | Markov chains (PDF) |
| 33 | Entropy (PDF) |
| 34 | Martingales and the optional stopping time theorem (PDF) |
| 35 | Martingales and risk neutral probability (PDF) |
| 36 | Risk neutral probability and Black-Scholes (PDF) |
| 37 | Review for final exam I (PDF) |
| 38 | Review for final exam II (PDF) |
| 39 | Review for final exam III (PDF) |
