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### Probability and Counting

00:46:29Joseph BlitzsteinSample spaces, naive definition of probability, counting, sampling.

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### Story Proofs, Axioms of Probability

00:45:40Joseph BlitzsteinBose-Einstein, story proofs, Vandermonde identity, axioms of probability.

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### Birthday Problem, Properties of Probability

00:48:55Joseph BlitzsteinBirthday problems, properties of probability, Inclusion-exclusion, matching problem.

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### Conditional Probability

00:49:45Joseph BlitzsteinLaw of total probability, conditional probability examples, conditional independence.

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### Conditioning Continued, Law of Total Probability

00:50:02Joseph BlitzsteinLaw of total probability, conditional probability examples, conditional independence.

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### Gambler's Ruin and Random Variables

00:51:46Joseph BlitzsteinGambler's ruin, first step analysis, random variables, Bernoulli, Binomial.

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### Random Variables and Their Distributions

00:50:24Joseph BlitzsteinRandom variables, CDFs, PMFs, discrete vs. continuous, Hypergeometric.

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### Expectation, Indicator Random Variables, Linearity

00:50:23Joseph BlitzsteinIndependence, Geometric, expected values, indicator r.v.s, linearity, symmetry, fundamental bridge.

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### Expectation Continued

00:50:10Joseph BlitzsteinLinearity, Putnam problem, Negative Binomial, St. Petersburg paradox.

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### The Poisson Distribution

00:42:46Joseph BlitzsteinSympathetic magic, Poisson distribution, Poisson approximation.

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### Discrete vs. Continuous, the Uniform

00:49:57Joseph BlitzsteinDiscrete vs. continuous distributions, PDFs, variance, standard deviation, Uniform universality.

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### Moment Generating Functions

00:50:45Joseph BlitzsteinMoment generating functions(MGFs), hybrid Bayes' rule, Laplace's rule of sucession.

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### Moment Generating Functions Continued

00:49:41Joseph BlitzsteinMGFs to get moments of Expo and Normal, sums of Poissons, joint distributions.

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### Joint, Conditional, and Marginal Distributions

00:50:09Joseph BlitzsteinJoint, conditional, and marginal distributions, 2-D LOTUS, expected distance between Uniforms, chicken-egg.

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### Multinominal and Caucchy

00:49:00Joseph BlitzsteinExpected distance between Normals, Multinomial, Cauchy.

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### Covariance and Correlation

00:49:26Joseph BlitzsteinCovariance, correlation, variance of a sum, variance of Hypergeometric.

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### Transformations and Convolutions

00:47:46Joseph BlitzsteinTransformations, LogNormal, convolutions, proving existence.

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### Beta Distribution

00:49:48Joseph BlitzsteinBeta distribution, Bayes' billards, finance preview and examples.

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### Gamma Distribution and Poisson Process

00:48:49Joseph BlitzsteinGamma distribution, Poisson processes.

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### Order Statistics and Conditional Expectation

00:48:15Joseph BlitzsteinBeta-Gamma(bank-post office), order statistics, conditional expectation, two envelope paradox.

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### Conditional Expectation Continued

00:49:53Joseph BlitzsteinTwo envelope paradox(cont.), conditional expectation(cont.), waiting for HT vs. waiting for HH.

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### Conditional Expectation Given an R.V.

00:50:34Joseph BlitzsteinConditional expectation(cont.), taking out what's known, Adam's law, Eve's law, projection picture.

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### Inequalities

00:47:29Joseph BlitzsteinSum of random numbers of random variables, inequalities(Cauchy-Schwarz, Jensen, Markov, Chebyshev).

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### Law of Large Numbers and Central Limit Theorem

00:49:48Joseph BlitzsteinLaw of large numbers, central limit theorem.

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### Chi-Square, Student-t, Multivariate Normal

00:47:28Joseph BlitzsteinChi-Square, Student-t, Multivariate Normal.

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### Markov Chains Continued

00:48:24Joseph BlitzsteinMarkov chains(cont.), irreducibility, recurrence, transience, reversibility, random walk on an undirected network.

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### Markov Chains Continued Futher

00:47:01Joseph BlitzsteinMarkov chains(cont.), Google PageRank as a Markov chain.

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### A Look Ahead

00:36:59Joseph BlitzsteinA look ahead, final review, other statistics courses, regression example, sampling from a finite population example.