• ### Lecture 34: A Look Ahead | Statistics 110

We look ahead to possible future courses in statistics, discussing a few out of a very large number of connections between Stat 110 and other statistics idea...

• ### Lecture 33: Markov Chains Continued Further | Statistics 110

We continue to explore Markov chains, and show how Google PageRank can be understood in terms of a natural Markov chain on the web.

• ### Lecture 23: Beta Distribution | Statistics 110

We introduce the Beta distribution and show how it is the conjugate prior for the Binomial, and discuss Bayes' billiards. Stephen Blyth then gives examples o...

• ### Lecture 20: Multinomial And Cauchy | Statistics 110

We introduce the Multinomial distribution, which is arguably the most important multivariate discrete distribution, and discuss its story and some of its nic...

• ### Lecture 32: Markov Chains Continued | Statistics 110

We continue to explore Markov chains, and discuss irreducibility, recurrence and transience, reversibility, and random walk on an undirected network.

• ### Lecture 29: Law Of Large Numbers And Central Limit Theorem | Statistics 110

We introduce and prove versions of the Law of Large Numbers and Central Limit Theorem, which are two of the most famous and important theorems in all of stat...

• ### Lecture 24: Gamma Distribution And Poisson Process | Statistics 110

We introduce the Gamma distribution and discuss the connection between the Gamma distribution and Poisson processes.

• ### Stat 110 Harvard - Let's Get Started (Statistics Song)

music video for the theme song by Stephen Kent for Stat 110: Introduction to Probability, taught by Joe Blitzstein at Harvard. The full course (including 34 ...

• ### Lecture 27: Conditional Expectation Given An R.V. | Statistics 110

We show how to think about a conditional expectation E(Y|X) of one r.v. given another r.v., and discuss key properties such as taking out what's known, Adam'...

• ### Lecture 30: Chi-Square, Student-t, Multivariate Normal | Statistics 110

We introduce several important offshoots of the Normal: the Chi-Square, Student-t, and Multivariate Normal distributions.

• ### Lecture 18: MGFs Continued | Statistics 110

We use MGFs to get moments of Exponential and Normal distributions, and to get the distribution of a sum of Poissons. We also start on joint distributions.

• ### Lecture 26: Conditional Expectation Continued | Statistics 110

We peek further into the Two Envelope Paradox, and continue to explore conditional expectation, while considering waiting for HT vs. waiting for HH, in flips...

• ### Lecture 17: Moment Generating Functions | Statistics 110

We introduce moment generating functions (MGFs), which have many uses in probability. We also discuss Laplace's rule of succession and the "hybrid" version o...

• ### Lecture 21: Covariance And Correlation | Statistics 110

We introduce covariance and correlation, and show how to obtain the variance of a sum, including the variance of a Hypergeometric random variable.

• ### Lecture 28: Inequalities | Statistics 110

We consider the sum of a random number of random variable (e.g., with customers in a store). We then introduce 4 useful inequalities: Cauchy-Schwarz, Jensen,...

• ### Lecture 19: Joint, Conditional, And Marginal Distributions | Statistics 110

We discuss joint, conditional, and marginal distributions (continuing from Lecture 18), the 2-D LOTUS, the fact that E(XY)=E(X)E(Y) if X and Y are independen...

• ### Lecture 12: Discrete Vs. Continuous, The Uniform | Statistics 110

We compare discrete vs. continuous distributions, and discuss probability density functions (PDFs), variance, standard deviation, and the Uniform distribution.

• ### Lecture 15: Midterm Review | Statistics 110

We work through some extra examples, such as the coupon collector problem, an example of Universality of the Uniform, an example of LOTUS, and a Poisson proc...

• ### Lecture 14: Location, Scale, And LOTUS | Statistics 110

We discuss location and scale, and standardization. We also make a conscious effort to describe the Law of the Unconscious Statistician (LOTUS), and use it t...

• ### Lecture 11: The Poisson Distribution | Statistics 110

We introduce the Poisson distribution, which is arguably the most important discrete distribution in all of statistics. We explore its uses as an approximate...

• ### Lecture 25: Order Statistics And Conditional Expectation | Statistics 110

We show how Beta and Gamma are connected (via the bank-post office story), and introduce order statistics. We then start on conditional expectation, with a p...