| 1 |
Permutations and combinations |
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| 2 |
Multinomial coefficients and more counting |
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| 3 |
Sample spaces and set theory |
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| 4 |
Axioms of probability |
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| 5 |
Probability and equal likelihood |
Problem Set 1 due |
| 6 |
Conditional probabilities |
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| 7 |
Bayes' formula and independent events |
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| 8 |
Discrete random variables |
Problem Set 2 due |
| 9 |
Expectations of discrete random variables |
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| 10 |
Variance |
Problem Set 3 due |
| 11 |
Binomial random variables, repeated trials and the so-called modern portfolio theory |
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| 12 |
Poisson random variables |
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| 13 |
Poisson processes |
Problem Set 4 due |
| 14 |
More discrete random variables |
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| 15 |
Review for midterm exam 1 |
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| 16 |
Midterm exam 1 |
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| 17 |
Continuous random variables |
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| 18 |
Normal random variables |
Problem Set 5 due |
| 19 |
Exponential random variables |
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| 20 |
More continuous random variables |
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| 21 |
Joint distribution functions |
Problem Set 6 due |
| 22 |
Sums of independent random variables |
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| 23 |
Expectation of sums |
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| 24 |
Covariance and some conditional expectation exercises |
Problem Set 7 due |
| 25 |
Conditional expectation |
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| 26 |
Moment generating functions |
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| 27 |
Weak law of large numbers |
Problem Set 8 due |
| 28 |
Review for midterm exam 2 |
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| 29 |
Midterm exam 2 |
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| 30 |
Central limit theorem |
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| 31 |
Strong law of large numbers and Jensen's inequality |
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| 32 |
Markov chains |
Problem Set 9 due |
| 33 |
Entropy |
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| 34 |
Martingales and the optional stopping time theorem |
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| 35 |
Martingales and risk neutral probability |
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| 36 |
Risk neutral probability and Black-Scholes |
|
| 37 |
Review for final exam |
Problem Set 10 due |
| 38 |
Review for final exam (cont.) |
|
| 39 |
Review for final exam (cont.) |
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| 40 |
Final exam |
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