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source: Harvard University Last updated on 2014年7月2日

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. 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.

Lecture 1: Probability and Counting | Statistics 110 46:29

Lecture 2: Story Proofs, Axioms of Probability 45:40

Lecture 3: Birthday Problem, Properties of Probability 48:55

Lecture 4: Conditional Probability 49:45

Lecture 5: Conditioning Continued, Law of Total Probability 50:02

Lecture 6: Monty Hall, Simpson's Paradox 49:01

Lecture 7: Gambler's Ruin and Random Variables 51:46

Lecture 8: Random Variables and Their Distributions 50:24

Lecture 9: Expectation, Indicator Random Variables, Linearity 50:23

Lecture 10: Expectation Continued 50:10

Lecture 11: The Poisson distribution 42:46

Lecture 12: Discrete vs. Continuous, the Uniform 49:56

Lecture 13: Normal distribution 51:10

Lecture 14: Location, Scale, and LOTUS 48:55

Lecture 15: Midterm Review 38:12

Lecture 16: Exponential Distribution 18:20

Lecture 17: Moment Generating Functions 50:45

Lecture 18: MGFs Continued 49:41

Lecture 19: Joint, Conditional, and Marginal Distributions 50:09

Lecture 20: Multinomial and Cauchy 49:00

Lecture 21: Covariance and Correlation 49:26

Lecture 22: Transformations and Convolutions 47:46

Lecture 23: Beta distribution 49:48

Lecture 24: Gamma distribution and Poisson process 48:49

Lecture 25: Order Statistics and Conditional Expectation 48:15

Lecture 26: Conditional Expectation Continued 49:53

Lecture 27: Conditional Expectation given an R.V. | 50:34

Lecture 28: Inequalities 47:29

Lecture 29: Law of Large Numbers and Central Limit Theorem 49:48

Lecture 30: Chi-Square, Student-t, Multivariate Normal 47:28

Lecture 31: Markov Chains 46:38

Lecture 32: Markov Chains Continued 48:24

Lecture 33: Markov Chains Continued Further 47:01

Lecture 34: A Look Ahead 36:59

Joseph Blitzstein: "The Soul of Statistics" | Harvard Thinks Big 4 14:47

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