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Last updated:

September 23, 2023

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Unlimited Duration

FREE

This course includes:

Unlimited Duration

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Description

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.

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.

https://www.youtube.com/watch?v=dzFf3r1yph8&ab_channel=HarvardUniversity

Course Curriculum

  • 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

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