Statistics 110: Probability (Joe Blitzstein / Harvard University)

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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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