| 1 |
Probabilistic models and probability measures |
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| 2 |
Two fundamental probabilistic models |
Homework 1 due |
| 3 |
Conditioning and independence |
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| 4 |
Counting |
Homework 2 due |
| 5 |
Random variables |
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| 6 |
Discrete random variables and their expectations |
Homework 3 due |
| 7 |
Discrete random variables and their expectations (cont.) |
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| 8 |
Continuous random variables |
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| 9 |
Continuous random variables (cont.) |
Homework 4 due |
| 10 |
Derived distributions |
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| 11 |
Abstract integration |
Homework 5 due |
| 12 |
Abstract integration (cont.) |
Homework 6 due |
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Midterm exam |
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| 13 |
Product measure and Fubini's theorem |
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| 14 |
Moment generating functions |
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| 15 |
Multivariate normal distributions |
Homework 7 due |
| 16 |
Multivariate normal distributions: characteristic functions |
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| 17 |
Convergence of random variables |
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| 18 |
Laws of large numbers |
Homework 8 due |
| 19 |
Laws of large numbers (cont.) |
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| 20 |
The Bernoulli and Poisson processes |
Homework 9 due |
| 21 |
The Poisson process |
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| 22 |
Markov chains |
Homework 10 due |
| 23 |
Markov chains II: mean recurrence times |
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| 24 |
Markov chains III: periodicity, mixing, absorption |
Homework 11 due |
| 25 |
Infinite Markov chains, continuous time Markov chains |
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| 26 |
Birth-death processes |
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