Math E-102 - Sets, Counting, and Probability

Math E-102 - Sets, Counting, and Probability (Fall 2005, Harvard Extension School). Instructor: Professor Paul G. Bamberg. This online math course develops the mathematics needed to formulate and analyze probability models for idealized situations drawn from everyday life. Topics include elementary set theory, techniques for systematic counting, axioms for probability, conditional probability, discrete random variables, infinite geometric series, and random walks. Applications to card games like bridge and poker, to gambling, to sports, to election results, and to inference in fields like history and genealogy, national security, and theology. The emphasis is on careful application of basic principles rather than on memorizing and using formulas.

Lecture 08 - Expectation I

Unconscious Statistician; Properties of Expectation; Binomial Expectation; Tail-Sum Theorem; Geometric Tail-Sum; Negative Binomial Expectation; Coupons Problem; Variance; Telescoping Series; Convergence.

Go to the Course Home or watch other lectures:

Lecture 01 - Probability, Intuition, and Axioms
Lecture 02 - Probability by Counting and Inclusion-Exclusion
Lecture 03 - Principles of Counting
Lecture 04 - Conditional Probability
Lecture 05 - Conditional Craps
Lecture 06 - Lying Witnesses and Simpson's Paradox
Lecture 07 - Random Variables
Lecture 08 - Expectation I
Lecture 09 - Expectation II
Lecture 10 - Tartan Dice; Terminated Geometric; Coin Tossing
Lecture 11 - Gambling
Lecture 12 - Expected Lead Time; Bijections Between Paths
Lecture 13 - Variables
Lecture 14 - Inequality
Lecture 15 - Questions