# Math 170A: General Course Outline

## Catalog Description

**170A. Probability Theory. (4) **

Lecture, three hours; discussion, one hour. Requisites: courses 32B, 33A, 131A. Not open to students with credit in course 170E, Electrical Engineering 131A or Statistics 100A. Rigorous presentation of probability theory based on real analysis. Probability space, probability and conditional probability, independence, Bayes? rule, discrete and continuous random variables and their distributions, expectation, moments and variance, conditional distribution and expectation, weak law of large numbers. P/NP or letter grading.

## Course Information:

The course discusses the foundations of probability as a mathematical discipline rooted in undergraduate real analysis. At the end of the course, the students will have the tools and ability to formulate, analyze an answer questions in probability and prove the validity of their reasoning in full mathematical rigor.

## Textbook

*Probability: An Introduction (2nd ed.). * by Grimmett, G. R., & Welsh, D. J. (2014).Oxford: Oxford University Press.

Outline update: T. Austin, 01/20

## Schedule of Lectures

Lecture | Section | Topics |
---|---|---|

Week 1 |
Sections 1.1-1.5, 1.9 |
Sample space, events, probability |

Week 2 |
Sections 1.6-1.7 |
Conditional probability and independence |

Week 3 |
Sections 1.8, 1.10 |
Partition theorem and Bayes rule, examples |

Week 4 |
Sections 2.1-2.4 |
Discrete random variables, their functions, expectation and variance |

Week 5 |
Sections 2.5, 3.1-3.2 |
Conditional expectation, multivariate discrete distributions |

Week 6 |
Sections 3.3-3.5 |
Independent discrete random variables, indicators |

Week 7 |
Sections 5.1-5.6 |
Cumulative distribution function, continuous random variables |

Week 8 |
Sections 6.1-6.4 |
Multivariate distributions and their marginals |

Week 9 |
Sections 6.5-6.7 |
Change of variables, conditional expectation |

Week 10 |
Sections 6.8, 7.3, 8.1-8.2 |
Mutlivariate normal distribution, weak law of large numbers |