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Lecture

# Markov Chains Continued Futher

Home > Mathematics > Statistics > Statistics 110: Probability > Markov Chains Continued Futher Lecture Details:

Markov chains(cont.), Google PageRank as a Markov chain.

Lectures:
• ### Probability and Counting

00:46:29Joseph Blitzstein

Sample spaces, naive definition of probability, counting, sampling.

• ### Story Proofs, Axioms of Probability

00:45:40Joseph Blitzstein

Bose-Einstein, story proofs, Vandermonde identity, axioms of probability.

• ### Birthday Problem, Properties of Probability

00:48:55Joseph Blitzstein

Birthday problems, properties of probability, Inclusion-exclusion, matching problem.

• ### Conditional Probability

00:49:45Joseph Blitzstein

Law of total probability, conditional probability examples, conditional independence.

• ### Conditioning Continued, Law of Total Probability

00:50:02Joseph Blitzstein

Law of total probability, conditional probability examples, conditional independence.

• ### Monty hall, Simpson's Paradox

00:49:01Joseph Blitzstein

• ### Gambler's Ruin and Random Variables

00:51:46Joseph Blitzstein

Gambler's ruin, first step analysis, random variables, Bernoulli, Binomial.

• ### Random Variables and Their Distributions

00:50:24Joseph Blitzstein

Random variables, CDFs, PMFs, discrete vs. continuous, Hypergeometric.

• ### Expectation, Indicator Random Variables, Linearity

00:50:23Joseph Blitzstein

Independence, Geometric, expected values, indicator r.v.s, linearity, symmetry, fundamental bridge.

• ### Expectation Continued

00:50:10Joseph Blitzstein

Linearity, Putnam problem, Negative Binomial, St. Petersburg paradox.

• ### The Poisson Distribution

00:42:46Joseph Blitzstein

Sympathetic magic, Poisson distribution, Poisson approximation.

• ### Discrete vs. Continuous, the Uniform

00:49:57Joseph Blitzstein

Discrete vs. continuous distributions, PDFs, variance, standard deviation, Uniform universality.

• ### Normal Distribution

00:51:10Joseph Blitzstein

Standard Normal, Normal normalizing constant.

• ### Location, Scale and LOTUS

00:48:55Joseph Blitzstein

Normal distribution, standardization, LOTUS.

• ### Midterm Review

00:38:12Joseph Blitzstein

Midterm review, extra examples.

• ### Exponential Distribution

00:18:19Joseph Blitzstein

Exponential distribution, memoryless property.

• ### Moment Generating Functions

00:50:45Joseph Blitzstein

Moment generating functions(MGFs), hybrid Bayes' rule, Laplace's rule of sucession.

• ### Moment Generating Functions Continued

00:49:41Joseph Blitzstein

MGFs to get moments of Expo and Normal, sums of Poissons, joint distributions.

• ### Joint, Conditional, and Marginal Distributions

00:50:09Joseph Blitzstein

Joint, conditional, and marginal distributions, 2-D LOTUS, expected distance between Uniforms, chicken-egg.

• ### Multinominal and Caucchy

00:49:00Joseph Blitzstein

Expected distance between Normals, Multinomial, Cauchy.

• ### Covariance and Correlation

00:49:26Joseph Blitzstein

Covariance, correlation, variance of a sum, variance of Hypergeometric.

• ### Transformations and Convolutions

00:47:46Joseph Blitzstein

Transformations, LogNormal, convolutions, proving existence.

• ### Beta Distribution

00:49:48Joseph Blitzstein

Beta distribution, Bayes' billards, finance preview and examples.

• ### Gamma Distribution and Poisson Process

00:48:49Joseph Blitzstein

Gamma distribution, Poisson processes.

• ### Order Statistics and Conditional Expectation

00:48:15Joseph Blitzstein

Beta-Gamma(bank-post office), order statistics, conditional expectation, two envelope paradox.

• ### Conditional Expectation Continued

00:49:53Joseph Blitzstein

Two envelope paradox(cont.), conditional expectation(cont.), waiting for HT vs. waiting for HH.

• ### Conditional Expectation Given an R.V.

00:50:34Joseph Blitzstein

Conditional expectation(cont.), taking out what's known, Adam's law, Eve's law, projection picture.

• ### Inequalities

00:47:29Joseph Blitzstein

Sum of random numbers of random variables, inequalities(Cauchy-Schwarz, Jensen, Markov, Chebyshev).

• ### Law of Large Numbers and Central Limit Theorem

00:49:48Joseph Blitzstein

Law of large numbers, central limit theorem.

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

00:47:28Joseph Blitzstein

Chi-Square, Student-t, Multivariate Normal.

• ### Markov Chains

00:46:38

Markov chains, transition matrix, stationery distribution.

• ### Markov Chains Continued

00:48:24Joseph Blitzstein

Markov chains(cont.), irreducibility, recurrence, transience, reversibility, random walk on an undirected network.

• ### Markov Chains Continued Futher

00:47:01Joseph Blitzstein

Markov chains(cont.), Google PageRank as a Markov chain.