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Math 170A: General Course Outline

Catalog Description

170A. Probability Theory. (4) Lecture, three hours; discussion, one hour. Requisites: courses 32B, 33A. Not open to students with credit for Electrical Engineering 131A or Statistics 100A. Probability distributions, random variables and vectors, expectation. P/NP or letter grading.

Additional Information Probability and stochastic processes are used to create and analyze models in a broad range of fields, including statistics, economics, finance, engineering, biology and physics. Mathematics 170AB and 171 are designed to give a firm foundation in this area for students who will work and/or do graduate work in one of these fields. They also provide an excellent background for graduate work in probability and related areas of mathematics.

These courses are particularly well suited to students who plan to take the exams in actuarial science. The second exam in this series (number 110) is on probability and statistics. Mathematics 170AB covers roughly 2/3 of the material on that exam.

Course 170A is multiply listed with Statistics. Usually, two sections are offered each Fall Quarter, one by Mathematics and one by Statistics. Total enrollment in the two sections tends to be about 50.

The three courses are intended as a year-long sequence. However, it is possible, and not unusual, to take 171 without 170B. In fact, the enrollments in 171 are sometimes larger than in 170B (both are in the 10-20 range). Mathematics 170B is offered each Winter Quarter, and Mathematics 171 is offered each Spring.

Textbook

Introduction to Probability by D. P. Bertsekas and John N. Tsitsiklis, 2nd edition

Comments:

The theoretical problems, which appear with full solutions at the ends of the chapters, are an essential part of the course. Many of them should be incorporated into the lectures.

Unfortunately, solutions to all of the other problems are freely available on the book?s web site. Additional problems (with no posted solutions) are available at http://www.athenasc.com/prob-supp.html

Outline T. Liggett 4/10

Schedule of Lectures

Lecture Section Topics

1

1.1

Sets

2-3

1.2

Probabilistic Models

4-5

1.3

Conditional Probability

6

1.4

Total Probability Theorem and Bayes Rule

7-8

1.5

Independence

9

1.6

Counting

10

Midterm Exam

11-12

2.1, 2.2

Discrete Random Variables; Probability Mass Functions

13-14

2.3, 2.4

Functions of Random Variables; Expectation and Variance

15

2.5, 4.2

Joint PMFs of Multiple Random Variables; Covariance in the Computation of the Variance of a Sum

16-17

2.6

Conditioning

18-19

2.7

Independence

20

Midterm Exam

21-22

3.1

Continuous Random Variables and PDFs

23

3.2

Cumulative Distribution Functions

24

3.3

Normal Random Variables

25

3.4

Joint PDFs of Multiple Random Variables

26-27

3.5

Conditioning

28

3.6

The Continuous Bayes Rule