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Probability and Statistics – Class 1

Harvard University

Lessons

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Lesson 1: Probability and Counting

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Lesson 2: Story Proofs, Axioms of Probability

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Lesson 3: Birthday Problem, Properties of Probability

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Lesson 4: Conditional Probability

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Lesson 5: Conditioning Continued, Law of Total Probability

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Lesson 6: Monty Hall, Simpson’s Paradox

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Lesson 7: Gambler’s Ruin and Random Variables

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Lesson 8: Random Variables and Their Distributions

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Lesson 9: Expectation, Indicator Random Variables, Linearity

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Lesson 10: Expectation Continued

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Lesson 11: The Poisson distribution

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Lesson 12: Discrete vs. Continuous, the Uniform

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Lesson 13: Normal distribution

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Lesson 14: Location, Scale, and LOTUS

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Lesson 15: Midterm Review

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Lesson 16: Exponential Distribution

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Lesson 17: Moment Generating Functions

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Lesson 18: MGFs Continued

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Lesson 19: Joint, Conditional, and Marginal Distributions

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Lesson 20: Multinomial and Cauchy

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Lesson 21: Covariance and Correlation

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Lesson 22: Transformations and Convolutions

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Lesson 23: Beta distribution

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Lesson 24: Gamma distribution and Poisson process

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Lesson 25: Order Statistics and Conditional Expectation

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Lesson 26: Conditional Expectation Continued

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Lesson 27: Conditional Expectation given an R.V.

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Lesson 28: Inequalities

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Lesson 29: Law of Large Numbers and Central Limit Theorem

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Lesson 30: Chi-Square, Student-t, Multivariate Normal

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Lesson 31: Markov Chains

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Lesson 32: Markov Chains Continued

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Lesson 33: Markov Chains Continued Further

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Lesson 34: A Look Ahead

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Lesson 35: Joseph Blitzstein: “The Soul of Statistics”