Math 477:01 -- Fall 2007

Date | Sections | Topics |
---|---|---|

9/4 | 1.1--1.5 | Combinatorics |

9/7 | 1.6--2.3 | Indistinguishable objects; axioms of probability |

9/11 | 2.4, 2.5 | Inclusion/exclusion formula; equally likely outcomes |

9/14 | 2.5 | More examples; Stirling's approximation |

9/18 | 3.1--3.3 | Conditional probability and Bayes' formula |

9/21 | 3.4 | Independent events |

9/25 | 3.4, 3.5 | Repeated independent trials |

9/28 | 4.1--4.2 | Random variables and distribution functions |

10/2 | 4.3--4.5 | Expectation and variance of discrete random variables |

10/5 | 4.6, 4.8.1 | Bernoulli, binomial, and geometric random variables |

10/9 | EXAM 1 |
All material covered through lecture of 10/2 |

10/12 | 4.7, 4.9.2, 4.9.3 | Poisson, negative binomial, and hypergeometric random variables |

10/16 | 5.1, 5.2 | Continuous random variables; expectation, variance |

10/19 | 5.3--5.5 | Uniform, exponential, and normal random variables |

10/23 | 5.4.1 | Normal approximation to binomial random variables |

10/26 | 5.6.1, 5.7 | Gamma random variable; functions of a random variable |

10/30 | 6.1 | Joint distributions of several random variables |

11/2 | 6.2 | Independent random variables |

11/6 | 6.3 | Sums of independent random variables |

11/9 | 7.1--7.3 | Linearity of expectation |

11/13 | EXAM 2 |
All material covered through lecture of 11/6 |

11/16 | 7.4 | Covariance and correlation |

11/21 | 6.4, 6.5 | Conditional distributions |

11/27 | 7.5 | Conditional expectation |

11/30 | 7.7 | Moment generating functions |

12/4 | 8.1--8.2 | Markov and Chebyshev inequalities; weak law of large numbers |

12/7 | 8.3 | The central limit theorem |

12/11 | 8.3 | Proof of the central limit theorem; examples. |

12/18 | FINAL EXAM |
8:00 A.M.--11:00 A.M. |