# YouTube [Stat 110 playlist on YouTube](https://www.youtube.com/playlist?list=PL2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) **Table of Contents** [Lecture 1: sample spaces, naive definition of probability, counting, sampling](https://www.youtube.com/watch?v=KbB0FjPg0mw&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 2: Bose-Einstein, story proofs, Vandermonde identity, axioms of probability](https://www.youtube.com/watch?v=FJd_1H3rZGg&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 3: birthday problem, properties of probability, inclusion-exclusion, matching problem](https://www.youtube.com/watch?v=LZ5Wergp_PA&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo&index=3) [Lecture 4: independence, Newton-Pepys, conditional probability, Bayes’ rule](https://www.youtube.com/watch?v=P7NE4WF8j-Q&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 5: law of total probability, conditional probability examples, conditional independence](https://www.youtube.com/watch?v=JzDvVgNDxo8&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 6: Monty Hall problem, Simpson’s paradox](https://www.youtube.com/watch?v=fDcjhAKuhqQ&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 7: gambler’s ruin, first step analysis, random variables, Bernoulli, Binomial](https://www.youtube.com/watch?v=PNrqCdslGi4&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 8: random variables, CDFs, PMFs, Hypergeometric](https://www.youtube.com/watch?v=k2BB0p8byGA&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 9: independence, Geometric, expected values, indicator r.v.s, linearity, symmetry, fundamental bridge](https://www.youtube.com/watch?v=LX2q356N2rU&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 10: linearity, Putnam problem, Negative Binomial, St. Petersburg paradox](https://www.youtube.com/watch?v=P1fSFvhPf7Q&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 11: sympathetic magic, Poisson distribution, Poisson approximation](https://www.youtube.com/watch?v=TD1N4hxqMzY&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 12: discrete vs. continuous, PDFs, variance, standard deviation, Uniform, universality](https://www.youtube.com/watch?v=Tci---bVs60&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 13: standard Normal, Normal normalizing constant](https://www.youtube.com/watch?v=72QjzHnYvL0&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 14: Normal distribution, standardization, LOTUS](https://www.youtube.com/watch?v=9vp1Ll2NpRw&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 15: midterm review, extra examples](https://www.youtube.com/watch?v=yFRZf81sB5k&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 16: Exponential distribution, memoryless property](https://www.youtube.com/watch?v=bM6nFDjvEns&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 17: moment generating functions (MGFs), hybrid Bayes’ rule, Laplace’s rule of succession](https://www.youtube.com/watch?v=N8O6zd6vTZ8&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 18: MGFs to get moments of Expo and Normal, sums of Poissons, joint distributions](https://www.youtube.com/watch?v=tVDdx6xUOcs&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 19: joint, conditional, and marginal distributions, 2-D LOTUS, chicken-egg](https://www.youtube.com/watch?v=J70dP_AECzQ&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 20: expected distance between Normals, Multinomial, Cauchy](https://www.youtube.com/watch?v=xiVWNkQUqKk&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 21: covariance, correlation, variance of a sum, variance of Hypergeometric](https://www.youtube.com/watch?v=IujCYxtpszU&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 22: transformations, LogNormal, convolutions, the probabilistic method](https://www.youtube.com/watch?v=yXwPUAIvFyg&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 23: Beta distribution, Bayes’ billiards, finance preview and examples](https://www.youtube.com/watch?v=UZjlBQbV1KU&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 24: Gamma distribution, Poisson processes](https://www.youtube.com/watch?v=Qjeswpm0cWY&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 25: Beta-Gamma (bank-post office), order statistics, conditional expectation, two envelope paradox](https://www.youtube.com/watch?v=2LR5JYbhyjg&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 26: two envelope paradox (cont.), conditional expectation (cont.), waiting for HT vs. waiting for HH](https://www.youtube.com/watch?v=PgawcWisb0I&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 27: conditional expectation (cont.), taking out what’s known, Adam’s law, Eve’s law](https://www.youtube.com/watch?v=gjBvCiRt8QA&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 28: sum of a random number of random variables, inequalities (Cauchy-Schwarz, Jensen, Markov, Chebyshev)](https://www.youtube.com/watch?v=UtXK_EQ3Pow&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 29: law of large numbers, central limit theorem](https://www.youtube.com/watch?v=OprNqnHsVIA&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 30: Chi-Square, Student-t, Multivariate Normal](https://www.youtube.com/watch?v=MF-XSJOsGqw&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 31: Markov chains, transition matrix, stationary distribution](https://www.youtube.com/watch?v=8AJPs3gvNlY&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 32: Markov chains (cont.), irreducibility, reversibility, random walk on an undirected network](https://www.youtube.com/watch?v=aBGOyZv2pZE&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 33: Markov chains (cont.), Google PageRank as a Markov chain](https://www.youtube.com/watch?v=Q-pCzTpwPBU&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo) [Lecture 34: a look ahead](https://www.youtube.com/watch?v=ChS3K2O-h7o&list=EC2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo)