Probability and Counting
46:29Story Proofs, Axioms of Probability
45:40Birthday Problem, Properties of Probability
48:54Conditional Probability
49:45Conditioning Continued, Law of Total Probability
50:01Monty Hall, Simpson's Paradox
49:00Gambler's Ruin and Random Variables
51:45Random Variables and Their Distributions
50:24Expectation, Indicator Random Variables, Linearity
50:23Expectation Continued
50:10The Poisson Distribution
42:46Discrete vs. Continuous, the Uniform
49:56Normal Distribution
51:10Location, Scale, and LOTUS
48:55Exponential Distribution
18:19Moment Generating Functions
50:45MGFs Continued
49:41Joint, Conditional, and Marginal Distributions
50:09Multinomial and Cauchy
49:00Covariance and Correlation
49:26Transformations and Convolutions
47:46Story Proofs, Axioms of Probability
Professor of the Practice in Statistics
This lecture introduces combinatorial 'story proofs' as a method for establishing identities like Vandermonde's identity, emphasizing intuitive insight over algebraic manipulation. It then lays the foundational axioms of probability theory, including discussion of Bose-Einstein sampling.
We fill in the "Bose-Einstein" entry of the sampling table, and discuss story proofs. For example, proving Vandermonde's identity with a story is easier and more insightful than going through a tedious algebraic derivation. We then introduce the axioms of probability.
Probability and Counting
Next · Lecture 3Birthday Problem, Properties of Probability