Week # | lectures | recitations | key Dates |
---|---|---|---|

1 | L1: Introduction. Probability, Spaces, and Sigma-Algebras | R1 | |

2 |
L2: Measures. Carathéodory. Lebesgue Measure and Infinite Coin Flips L3: Conditioning and Independence. Borel-Cantelli |
R2 | Homework 1 due |

3 |
L4: Measurable Functions. Random Variables. Cumulative Distribution Functions L5: Discrete Random Variables |
No recitation | Homework 2 due |

4 |
L6: Covariance and Correlation. Inclusion-Exclusion Formula, Examples L7: Abstract Integration |
R3 | Homework 3 due |

5 |
L8: Monotone and Dominated Convergence Theorems. Fatou’s Lemma L9: Product Measure. Fubini’s Theorem |
R4 | Homework 4 due |

6 | L10: Continous Random Variables, Examples | R5 | Homework 5 due |

7 |
L11: Continous Random Variables. Joint Distributions. Conditioning L12: Derived Distributions |
R6 | Homework 6 due |

8 | L13: Transforms. Moment Generating and Characteristic Functions | R7 | |

9 |
L14: Multivariate Normal L15: Multivariate Normal. Characteristic Functions |
R8 | Homework 7 due |

10 |
L16: Convergence of Random Variables L17: Weak Law of Large Numbers (WLLN) and Central Limit Theorem (CLT) |
R9 | Homework 8 due |

11 | L18: Strong Law of Large Numbers (SLLN). Chernoff Bounds | R10 | |

12 |
L19: Uniform Integrability. Kolmogorov 0–1 Law. Convergence of Series L20: Stochastic Processes: Bernoulli and Poisson |
No recitation | Homework 9 due |

13 |
L21: Markov Chains I L22: Markov Chains II |
R11 | Homework 10 due |

14 |
L23: Markov Chains III L24: Markov Chains IV |
R12 | Homework 11 due |

15 |
L25: Martingales I L26: Martingales II |
No recitation | Homework 12 (optional) |

16 | No lectures. | No recitation | Final Exam |

## Calendar

## Course Info

##### Instructor

##### As Taught In

Fall
2018

##### Level

##### Learning Resource Types

*grading*Exams

*notes*Lecture Notes

*assignment*Problem Sets