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1 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

2 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

3 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

4 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

5 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

6 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

7 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

8 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

9 probability W weak law of large numbers Weibull distribution Weierstrass theorem Y Yule-Simons distribution Z zeta-distribution Zipf distribution 韦维 - Zeta- 齐

Microsoft Word - Probability.doc

Microsoft Word - Probability.doc 十一機率 (Probability).... 分立變值 (discrete variate) 及連續變值 (continuous variate)..... 連續變質 (Continuous variate)/ 連續變數 (Continuous variable)..... 分立變值 (Discrete variate)/ 間斷變數 (Discrete variable)....