# Statistics 110: Probability

### Course Description

This course is an introduction to probability as a language and set of tools for understanding statistics, science, risk, and randomness. The ideas and methods are useful in statistics, science, engineering, economics, finance, and everyday life. Topics include the following. Basics: sample spaces and events, conditioning, Bayes' Theorem. Random variables and their distributions: distributions, moment generating functions, expectation, variance, covariance, correlation, conditional expectation. Univariate distributions: Normal, t, Binomial, Negative Binomial, Poisson, Beta, Gamma. Multivariate distributions: joint, conditional, and marginal distributions, independence, transformations, Multinomial, Multivariate Normal. Limit theorems: law of large numbers, central limit theorem. Markov chains: transition probabilities, stationary distributions, reversibility, convergence. Prerequisite: single variable calculus, familiarity with matrices.

Statistics 110 (Probability) has been taught at Harvard University by Joe Blitzstein (Professor of the Practice in Statistics, Harvard University) each year since 2006. The on-campus Stat 110 course has grown from 80 students to over 300 students per year in that time. Lecture videos, review materials, and over 250 practice problems with detailed solutions are provided.

Joe Blitzstein, Professor of the Practice in Statistics Harvard University, Department of Statistics
Not yet rated

### Video Lectures & Study Materials

Visit the official course website for more study materials: http://projects.iq.harvard.edu/stat110/home

# Lecture Play Lecture
1 Probability and Counting (46:29) Play Video
2 Story Proofs, Axioms of Probability (45:40) Play Video
3 Birthday Problem, Properties of Probability (48:55) Play Video
4 Conditional Probability (49:45) Play Video
5 Conditioning Continued, Law of Total Probability (50:02) Play Video
6 Monty Hall, Simpson's Paradox (49:01) Play Video
7 Gambler's Ruin and Random Variables (51:46) Play Video
8 Random Variables and Their Distributions (50:24) Play Video
9 Expectation, Indicator Random Variables, Linearity (50:23) Play Video
10 Expectation (Continued) (50:10) Play Video
11 The Poisson distribution (42:46) Play Video
12 Discrete vs. Continuous, the Uniform (49:56) Play Video
13 Normal Distribution (51:10) Play Video
14 Location, Scale, and LOTUS (48:55) Play Video
15 Midterm Review (38:12) Play Video
16 Exponential Distribution (18:20) Play Video
17 Moment Generating Functions (50:45) Play Video
18 MGFs (Continued) (49:41) Play Video
19 Joint, Conditional, and Marginal Distributions (50:09) Play Video
20 Multinomial and Cauchy (49:00) Play Video
21 Covariance and Correlation (49:26) Play Video
22 Transformations and Convolutions (47:46) Play Video
23 Beta distribution (49:48) Play Video
24 Gamma distribution and Poisson process (48:49) Play Video
25 Order Statistics and Conditional Expectation (48:15) Play Video
26 Conditional Expectation (Continued) (49:53) Play Video
27 Conditional Expectation given an R.V. (50:34) Play Video
28 Inequalities (47:29) Play Video
29 Law of Large Numbers and Central Limit Theorem (49:48) Play Video
30 Chi-Square, Student-t, Multivariate Normal (47:28) Play Video
31 Markov Chains (46:38) Play Video
32 Markov Chains (Continued) (48:24) Play Video
33 Markov Chains Continued Further (47:01) Play Video
34 Course Overview: A Look Ahead (36:59) Play Video
35 The Soul of Statistics (14:47) Play Video