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
47:46Gambler's Ruin and Random Variables
Professor of the Practice in Statistics
This lecture analyzes the classic Gambler's Ruin problem, modeling a finite-state absorbing Markov chain. It then introduces the fundamental concept of random variables and details the Bernoulli and Binomial probability distributions.
We analyze the gambler's ruin problem, in which two gamblers bet with each other until one goes broke. We then introduce random variables, which are essential in statistics and for the rest of the course, and start on the Bernoulli and Binomial distributions.
Monty Hall, Simpson's Paradox
Next · Lecture 8Random Variables and Their Distributions