| 1 |
Permutations and combinations |
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| 2 |
Multinomial coefficients and more counting |
|
| 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 |
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| 11 |
Binomial random variables, repeated trials and the so-called Modern Portfolio Theory |
Problem set 3 due |
| 12 |
Poisson random variables |
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| 13 |
Poisson processes |
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| 14 |
More discrete random variables |
Problem set 4 due |
| 15 |
Continuous random variables |
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| 16 |
Review for Midterm Exam 1 |
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| 17 |
Midterm Exam 1
|
|
| 18 |
Uniform random variables |
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| 19 |
Normal random variables |
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| 20 |
Exponential random variables |
Problem set 5 due |
| 21 |
More continuous random variables |
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| 22 |
Joint distribution functions |
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| 23 |
Sums of independent random variables |
Problem set 6 due |
| 24 |
Expectation of sums |
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| 25 |
Covariance |
|
| 26 |
Conditional expectation |
Problem set 7 due |
| 27 |
Moment generating distributions |
|
| 28 |
Review for Midterm Exam 2 |
|
| 29 |
Midterm Exam 2 |
|
| 30 |
Weak law of large numbers |
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| 31 |
Central limit theorem |
Problem set 8 due |
| 32 |
Strong law of large numbers and Jensen's inequality |
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| 33 |
Markov chains |
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| 34 |
Entropy |
Problem set 9 due |
| 35 |
Martingales and the Optional Stopping Time Theorem |
|
| 36 |
Risk Neutral Probability and Black-Scholes |
|
| 37 |
Review for Final Exam |
Problem Set 10 due, plus martingale note |
| 38 |
Review for Final Exam |
|
| 39 |
Review for Final Exam |
|
| 40 |
Final Exam |
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