Harvard Course , Prof. Joe Blitzstein

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Harvard Course , Prof. 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.

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We introduce sample spaces and the naive definition of probability (well get to the non-naive definition later). To apply the naive definition, we need to be able to count. So we introduce the multiplication rule, binomial coefficients, and the sampling table (for sampling with/without replacement when order does/doesnt matter).

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- 1.Lecture 1: Probability and Counting | Statistics 110
- 2.Lecture 2: Story Proofs, Axioms of Probability | Statistics 110
- 3.Lecture 3: Birthday Problem, Properties of Probability | Statistics 110
- 4.Lecture 4: Conditional Probability | Statistics 110
- 5.Lecture 5: Conditioning Continued, Law of Total Probability | Statistics 110
- 8.Lecture 8: Random Variables and Their Distributions | Statistics 110
- 9.Lecture 9: Expectation, Indicator Random Variables, Linearity | Statistics 110
- 10.Lecture 10: Expectation Continued | Statistics 110
- 11.Lecture 11: The Poisson distribution | Statistics 110
- 12.Lecture 12: Discrete vs. Continuous, the Uniform | Statistics 110
- 13.Lecture 13: Normal distribution | Statistics 110
- 14.Lecture 14: Location, Scale, and LOTUS | Statistics 110
- 15.Lecture 15: Midterm Review | Statistics 110
- 16.Lecture 16: Exponential Distribution | Statistics 110
- 17.Lecture 17: Moment Generating Functions | Statistics 110
- 18.Lecture 18: MGFs Continued | Statistics 110
- 19.Lecture 19: Joint, Conditional, and Marginal Distributions | Statistics 110
- 20.Lecture 20: Multinomial and Cauchy | Statistics 110
- 21.Lecture 21: Covariance and Correlation | Statistics 110
- 22.Lecture 22: Transformations and Convolutions | Statistics 110
- 23.Lecture 23: Beta distribution | Statistics 110
- 24.Lecture 24: Gamma distribution and Poisson process | Statistics 110
- 25.Lecture 25: Order Statistics and Conditional Expectation | Statistics 110
- 26.Lecture 26: Conditional Expectation Continued | Statistics 110
- 27.Lecture 27: Conditional Expectation given an R.V. | Statistics 110
- 28.Lecture 28: Inequalities | Statistics 110
- 29.Lecture 29: Law of Large Numbers and Central Limit Theorem | Statistics 110
- 30.Lecture 30: Chi-Square, Student-t, Multivariate Normal | Statistics 110
- 31.Lecture 31: Markov Chains | Statistics 110
- 32.Lecture 32: Markov Chains Continued | Statistics 110
- 33.Lecture 33: Markov Chains Continued Further | Statistics 110
- 34.Lecture 34: A Look Ahead | Statistics 110
- 35.Joseph Blitzstein: "The Soul of Statistics" | Harvard Thinks Big 4

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