probability A absolutely continuous random variables analytic theory of probability antithetic variables Archimedes Ars Conjectandi associative law for events axioms of probability axioms of surprise 绝 对 连 续 变 论 对 变 结 论 B ballot problem 选 问 题 Banach match problem 问 题 basic principle of counting 计 generalized 义 Bayes s formula 贝 Bernoulli random variables 变 Bernoulli trials 实 验 Bernstein polynomials 项 Bertand s paradox 贝 论 best prize problem beta distribution 贝 binary symmetric channel binomial coefficents 项 binomial random variables 项 变 normal approximation 态 approximation to hypergeometric computing its mass function 计 moments of 动 simulation of 拟 sums of independent 项 变 binomial theorem birthday problem 项 问 题
probability bivariate exponential distribution bivariate normal distribution Bonferroni s inequality Boole s inequality Box-Muller simulation technique Branching process Buffon s needle problem 态 费 罗 Box-Muller 拟 过 针 问 题 C Cantor distribution Cauchy distribution Cauchy - Schwarz inequality - center of gravity central limit theorem channel capacity Chapman-Kolmogorov equation 查 - 罗 Chebychev s inequality Chernoff bound 诺 chi-squared distribution density function relation to gamma distribution 马 simulation of 拟 coding theory 编 码 论 and entropy 熵 combination 组 combinatorial analysis 组 combinatorial identities 组 commutative law for events 换 complement of an event 补 complete graph 图 computing probabilities by conditioning 计 concave function conditional covariance formula 计 协 conditional distribution
probability continuous case 连 续 discrete case conditional expectation computing expectations by 计 conditioning conditional independence conditional probability conditional probability density function conditional probability mass function 质 conditional variance continuity correction 连 续 continuity property of probability 连 续 continuous random variable 连 续 变 control variate 变 convex function convolution 积 correlation correlation coefficient coupon collecting problems covariance cumulative distribution function D De Moivre-Laplace limit theorem DeMorgan s laws dependent events dependent random variables discrete random variables discrete uniform random variables distribution function distributive law for events dominant genes double exponential distribution 赠 问 题 协 积 - 变 变 变 显
probability Laplace distribution doubly stochastic matrix E entropy ergodic Markov chain evaluating evidence event exchangeable random variables expectation exponential random variable F failure rate function Fermat s combinatorial identity first moment frequency interpretation of probability G gambler s ruin problem game theory gamma distribution gamma function Guassian distribution genetics geometric random variable geometrical probability H Hamilton path hazard rate function hypergeometric random variables I importance sampling inclusion-exclusion independent events independent increment 阵 熵 历 马 链 换 换 变 变 费 马 组 动 论 频 释 赌 产 问 题 论 马 马 态 变 顿 风 险 变 样 过
probability independent random variables indicator random variables information interarrival times integer solutions of equations intersection of event inverse transform method J Jensen s inequality joint cumulative probability joint moment generating function joint probability density funciton joint probability mass function jointly continuous random variables K Keno knockout tournament L Laplace distribution Laplace s rule of succession law of frequency of errors law of total probability law of large numbers Legendre theorem limit of events linear prediction lognormal distribution M marginal distribution Markov chain Markov s inequality maximum likelihood estimates maximum-minimums identity 变 标 变 间 时 间 换 变 换 联 计 联 联 联 计 联 连 续 变 诺 赌 戏 赛 误 频 让 线 预 测 对 态 边 缘 马 链 马 计 值 值
probability mean of a random variable measurable events memoryless random variable midrange minimax theorem mode of random variable moment generating function moments of a random variable multinomial theorem multiplication rule of probability multivariate normal distribution mutually exclusive events N negative binomial random variables negative hypergeometric random noiseless coding theorem noisy coding theorem 变 值 测 记 忆 变 变 众 动 变 动 项 积 则 态 负 项 变 负 编 码 编 码 normal random variable null event null set O odds of an event order statistics P Parallel system partition Pascal permutations personal view of probability Poisson Poisson paradigm 态 变 顺 统 计 联 统 详 见 贝 论
probability Poisson process Poisson random variable poker polar algorithm Polya s urn model posterior probability prior probability probabilistic method probability of an event probability density function probability mass function problem of the points Q quick sort algorithm R random number random permutation random sample random subset random walk range of a random sample Rayleigh density function record value reduced sample space rejection method of simulation relative frequency definition of probability Riemann zeta function S sample mean sample median sample space sample variance sampling from a finite population 过 变 亚 验 验 质 问 题 样 样 值 记 录 值 对 频 义 Zeta 样 值 样 样 间 样 样
probability sampling with replacement sequential updating of information serve and rally games signal to noise ratio simulation standard deviation inequality standard normal distribution standard normal random variable stationary increments Stirling s approximation stochastically larger strong law of large numbers subjective probability subset superset T distribution function transition probabilities of a Markov chain trials triangular distribution twin problem U uncertainty uncorrelated random uniform random variable union of events unit normal random variable V value at risk variance Venn diagrams von Neumann 样 拟 标 标 态 标 态 变 稳 观 马 链 转 试 验 问 题 时 间 单 变 标 风 险 值 维 图 冯 诺
probability W weak law of large numbers Weibull distribution Weierstrass theorem Y Yule-Simons distribution Z zeta-distribution Zipf distribution 韦 维 - Zeta- 齐