Harvard Statistics 110 Homework Clipart

Statistics 110 (Probability), which 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.

Stat 110 playlist on YouTube

Table of Contents

Lecture 1: sample spaces, naive definition of probability, counting, sampling

Lecture 2: Bose-Einstein, story proofs, Vandermonde identity, axioms of probability

Lecture 3: birthday problem, properties of probability, inclusion-exclusion, matching problem

Lecture 4: independence, Newton-Pepys, conditional probability, Bayes’ rule

Lecture 5: law of total probability, conditional probability examples, conditional independence

Lecture 6: Monty Hall problem, Simpson’s paradox

Lecture 7: gambler’s ruin, first step analysis, random variables, Bernoulli, Binomial

Lecture 8: random variables, CDFs, PMFs, Hypergeometric

Lecture 9: independence, Geometric, expected values, indicator r.v.s, linearity, symmetry, fundamental bridge

Lecture 10: linearity, Putnam problem, Negative Binomial, St. Petersburg paradox

Lecture 11: sympathetic magic, Poisson distribution, Poisson approximation

Lecture 12: discrete vs. continuous, PDFs, variance, standard deviation, Uniform, universality

Lecture 13: standard Normal, Normal normalizing constant

Lecture 14: Normal distribution, standardization, LOTUS

Lecture 15: midterm review, extra examples

Lecture 16: Exponential distribution, memoryless property

Lecture 17: moment generating functions (MGFs), hybrid Bayes’ rule, Laplace’s rule of succession

Lecture 18: MGFs to get moments of Expo and Normal, sums of Poissons, joint distributions

Lecture 19: joint, conditional, and marginal distributions, 2-D LOTUS, chicken-egg

Lecture 20: expected distance between Normals, Multinomial, Cauchy

Lecture 21: covariance, correlation, variance of a sum, variance of Hypergeometric

Lecture 22: transformations, LogNormal, convolutions, the probabilistic method

Lecture 23: Beta distribution, Bayes’ billiards, finance preview and examples

Lecture 24: Gamma distribution, Poisson processes

Lecture 25: Beta-Gamma (bank-post office), order statistics, conditional expectation, two envelope paradox

Lecture 26: two envelope paradox (cont.), conditional expectation (cont.), waiting for HT vs. waiting for HH

Lecture 27: conditional expectation (cont.), taking out what’s known, Adam’s law, Eve’s law

Lecture 28: sum of a random number of random variables, inequalities (Cauchy-Schwarz, Jensen, Markov, Chebyshev)

Lecture 29: law of large numbers, central limit theorem

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

Lecture 31: Markov chains, transition matrix, stationary distribution

Lecture 32: Markov chains (cont.), irreducibility, reversibility, random walk on an undirected network

Lecture 33: Markov chains (cont.), Google PageRank as a Markov chain

Lecture 34: a look ahead

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