# Statistics 110: Probability

• Lecture 1: sample spaces〜起きうる場合を網羅したもの, naive definition of probability, counting, sampling〜数え上げ
• Lecture 2: Bose-Einstein, story proofs, Vandermonde identity, axioms of probability〜統計力学的な確率の考え方
• Lecture 3: birthday problem〜誕生日のパラドクス。同一誕生日の人が部屋の中にいることは結構ある, properties of probability, inclusion-exclusion, matching problem
• Lecture 4: independence, Newton-Pepys, conditional probability, Bayes’ rule〜サイコロで考える独立事象、条件付き確率、ベイズのルール
• Lecture 5: law of total probability, conditional probability examples, conditional independence〜全部足したら１になる。条件付き確率、条件付き独立
• Lecture 6: Monty Hall problem, Simpson’s paradoxモンティホール、シンプソンのパラドクス〜待ちあげやすい確率問題
• Lecture 7: gambler’s ruin, first step analysis, random variables, Bernoulli, Binomial〜次々に起きる確率事象
• Lecture 8: random variables, CDFs, PMFs, Hypergeometric〜確率変数とその分布
• Lecture 9: independence, Geometric, expected values, indicator random variables, linearity, symmetry, fundamental bridge〜独立と掛け算と期待値
• Lecture 10: linearity, Putnam problem, Negative Binomial, St. Petersburg paradox〜無限が入ると変な感じがしてくる
• Lecture 11: sympathetic magic, Poisson distribution, Poisson approximation〜類感呪術？？いつかは起きること
• Lecture 12: discrete vs. continuous, PDFs, variance, standard deviation, Uniform, universality〜離散変数から連続変数へ
• Lecture 13: standard Normal, Normal normalizing constant〜正規
• Lecture 14: Normal distribution, standardization, LOTUS〜正規分布
• Lecture 15: midterm review, extra examples〜中間試験
• Lecture 16: Exponential distribution, memoryless property〜無記憶性ということ
• Lecture 17: moment generating functions (MGFs), hybrid Bayes’ rule, Laplace’s rule of succession積率母関数、観察を続けて、さて、次を予想する
• Lecture 18: MGFs to get moments of Expo and Normal, sums of Poissons, joint distributions〜積率簿関数を使って確率分布を扱う
• Lecture 19: joint, conditional, and marginal distributions, 2-D LOTUS, chicken-egg〜分布を合わせる、分布で条件づける、周辺分布
• Lecture 20: expected distance between Normals, Multinomial, Cauchy〜分布間距離
• Lecture 21: covariance, correlation, variance of a sum, variance of Hypergeometric〜相互関係を数値化する
• Lecture 22: transformations, LogNormal, convolutions, the probabilistic method〜データ変換、畳み込み
• Lecture 23: Beta distribution, Bayes’ billiards, finance preview and examples〜二項観察とそのベイズ、β分布
• Lecture 24: Gamma distribution, Poisson processes〜ポアソン過程とそのベイズ、ガンマ分布
• Lecture 25: Beta-Gamma (bank-post office), order statistics, conditional expectation, two envelope paradox〜どちらがよいか
• Lecture 26: two envelope paradox (cont.), conditional expectation (cont.), waiting for HT vs. waiting for HH〜前回の続き
• Lecture 27: conditional expectation (cont.), taking out what’s known, Adam’s law, Eve’s law〜わかっていることに基づく期待
• Lecture 28: sum of a random number of random variables, inequalities (Cauchy-Schwarz, Jensen, Markov, Chebyshev)〜複数のランダム変数の和
• Lecture 29: law of large numbers, central limit theorem〜数が大きくなれば
• Lecture 30: Chi-Square, Student-t, Multivariate Normal〜漸近近似分布
• Lecture 31: Markov chains, transition matrix, stationary distribution〜状態推移、マルコフ連鎖
• Lecture 32: Markov chains (cont.), irreducibility, reversibility, random walk on an undirected network〜マルコフ連鎖ランダムウォーク
• Lecture 33: Markov chains (cont.), Google PageRank as a Markov chain〜グーグルのページランク手法とマルコフ連鎖
• Lecture 34: a look ahead〜さらにこの先へ