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Statistics 110: Probability (Harvard Univ.). Taught by Professor Joe Blitzstein, 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.
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English
English [CC]
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Description
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.
Course content
- Lecture 01 – Probability and Counting Unlimited
- Lecture 02 – Story Proofs, Axioms of Probability Unlimited
- Lecture 03 – Birthday Problem, Properties of Probability Unlimited
- Lecture 04 – Conditional Probability Unlimited
- Lecture 05 – Conditioning Continued, Law of Total Probability Unlimited
- Lecture 06 – Monty Hall, Simpson’s Paradox Unlimited
- Lecture 07 – Gambler’s Ruin and Random Variables Unlimited
- Lecture 08 – Random Variables and Their Distributions Unlimited
- Lecture 09 – Expectation, Indicator Random Variables, Linearity Unlimited
- Lecture 10 – Expectation Continued Unlimited
- Lecture 11 – The Poisson Distribution Unlimited
- Lecture 12 – Discrete vs. Continuous, the Uniform Unlimited
- Lecture 13 – Normal Distribution Unlimited
- Lecture 14 – Location, Scale, and LOTUS Unlimited
- Lecture 15 – Midterm Review Unlimited
- Lecture 16 – Exponential Distribution Unlimited
- Lecture 17 – Moment Generating Functions (MGFs) Unlimited
- Lecture 18 – MGFs Continued Unlimited
- Lecture 19 – Joint, Conditional, and Marginal Distributions Unlimited
- Lecture 20 – Multinomial and Cauchy Unlimited
- Lecture 21 – Covariance and Correlation Unlimited
- Lecture 22 – Transformations and Convolutions Unlimited
- Lecture 23 – Beta Distribution Unlimited
- Lecture 24 – Gamma Distribution and Poisson Process Unlimited
- Lecture 25 – Order Statistics and Conditional Expectation Unlimited
- Lecture 26 – Conditional Expectation Continued Unlimited
- Lecture 27 – Conditional Expectation given an R.V. Unlimited
- Lecture 28 – Inequalities Unlimited
- Lecture 29 – Law of Large Numbers and Central Limit Theorem Unlimited
- Lecture 30 – Chi-Square, Student-t, Multivariate Normal Unlimited
- Lecture 31 – Markov Chains Unlimited
- Lecture 32 – Markov Chains Continued Unlimited
- Lecture 33 – Markov Chains Continued Further Unlimited
- Lecture 34 – A Look Ahead Unlimited
Instructor
