1 | Permutations and combinations | |

2 | Multinomial coefficients and more counting | |

3 | Sample spaces and set theory | |

4 | Axioms of probability | |

5 | Probability and equal likelihood | Problem Set 1 due |

6 | Conditional probabilities | |

7 | Bayes' formula and independent events | |

8 | Discrete random variables | Problem Set 2 due |

9 | Expectations of discrete random variables | |

10 | Variance | |

11 | Binomial random variables, repeated trials and the so-called Modern Portfolio Theory | Problem Set 3 due |

12 | Poisson random variables | |

13 | Poisson processes | |

14 | More discrete random variables | Problem Set 4 due |

15 | Continuous random variables | |

16 | Review for Midterm Exam 1 | |

17 | Midterm Exam 1 | |

18 | Uniform random variables | |

19 | Normal random variables | |

20 | Exponential random variables | Problem Set 5 due |

21 | More continuous random variables | |

22 | Joint distribution functions | |

23 | Sums of independent random variables | Problem Set 6 due |

24 | Expectation of sums | |

25 | Covariance and correlation | |

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 | |

31 | Central limit theorem | Problem Set 8 due |

32 | Strong law of large numbers and Jensen's inequality | |

33 | Markov chains | |

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 |

38 | Review for Final Exam (cont.) | |

39 | Review for Final Exam (cont.) | |

40 | Final Exam | |