**Instructor**

**Overview**

CS206 is an introductory probability course. We will learn about combinatorics – different ways of counting events, discrete event probabilities, and, time-permitting, probabilities on continuous spaces.

Prerequisites: 198:205 and 640:152.

**Topics**

- Basic Ingredients (random experiment, sample space, events, probability measure).
- Conditional Probability, Bayes Theorem, Independence.
- Combinatorics and Counting.
- Recurrences, Generating Fns, and Applications.
- Random Variables.
- Bernoulli Trials.
- Expectation, Variance.
- Applications of Probability and Combinatorics.

**Schedule**

Topic | Description | Textbook |
---|---|---|

1 | Introduction | |

2 | Counting | Ross Ch.1 Rosen Ch.5 |

3 | Piegeonhole principle | Ross Ch.1 Rosen Ch.6 |

4 | Combinations and permutations Pascal's triangle | Ross Ch.1 Rosen Ch.6 |

5 | Ordered sampling with replacement Catalan numbers | Ross Ch.1 Rosen Ch.5 |

6 | Unordered sampling with replacement | Ross Ch.1 Rosen Ch.5 |

7 | Sampling algorithms | Rosen Ch. 5 |

8 | Probability | Ross, Ch.2 |

9 | Probability axioms | Ross, Ch.2 |

10 | Conditional probability | Ross, Ch. 3 |

11 | Bayes rule | Ross, Ch. 3 |

12 | Independence | Ross, Ch. 3 |

13 | Random variables | Ross, Ch.4 |

14 | Expecation and variance | Ross, Ch.4 |

15 | Binomial and Bernoulli random variable | Ross, Ch.4 |

16 | Poisson random variable | Ross, Ch.4 |

17 | Negative binomial random variable | Ross, Ch.4 |

18 | Continunous random variables | Ross, Ch.5 |

19 | Sampling of random variables | Ross, Ch. 10 |

20 | Gaussian random variable | Ross, Ch. 5 & 8 |

21 | Joint random variables | Ross, Ch. 6 |

22 | Transformation of random variables | Ross, Ch. 5 & 6 |

**Textbooks**

A First Course in Probability – Sheldon Ross, Prentice Hall, 9th ed., 2014.

Discrete Mathematics and its Applications – Kenneth A. Rosen

McGraw Hill, 7th ed., 2012 (Ch. 6-7)

**Other**

We use iClicker throughout the course.

You can also find an example of the course syllabus here. Note that I will be distributing a new syllabus, which may differ from the one linked here, each term.