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Math 70: General Course Outline

Course Description

70. Introduction to Probability. (4) Lecutre, 3 hours; Discussion, 1 hour. Requisites: courses 31A, 31B. Introduction to probability through applications and examples. Topics include laws of large numbers, statistics, chance trees, conditional probability, Bayes? rule, continuous and discrete random variables, jointly distributed random variables, multivariate normal and conditional distributions. In depth discussion of betting schemes in gambling, occurrence of rare events, coincidences and statistical predictions. P/NP or letter grading.

Course Information:

The course introduces a list of standard probabilistic problems and analyzes them in detail within the formalism of probability as a mathematical discipline. At the end of the course, the students will be able to demonstrate their understanding of the foundations and basic facts of probability as a mathematical discipline and apply them to resolve questions with probabilistic content.

Textbook(s)

Tijms, H. Understanding Probability, Chance Rules in Everyday Life, 3rd Edition. Cambridge University Press, 2012

Schedule of Lectures

Lecture Section Topics

Week 1

Ch. 1-2

Laws of large numbers and simulation

Week 2

Ch. 3-4

Probability in everyday life and rare events

Week 3

Ch. 5-6

Probability and statistics, chance trees

Week 4

Ch. 7

Foundations of probability

Week 5

Ch. 8

Conditional probability and Bayes? Rule

Week 6

Ch. 9

Discrete random variables

Week 7

Ch. 10

Continuous random variables

Week 8

Ch. 11

Jointly distributed random variables

Week 9

Ch. 12

Multivariate normals

Week 10

Ch. 13

Conditional distributions