概率论与统计学原理chapt1english
概率论与数理统计(chapt1-6 n重贝努利试验)
设A:恰好4次命中，B:至少4次命中，C:至多4次命中
（1） P( A) P5( 4) C54 0.840.2 0.4096
（2） P( B) P5( 4) P5( 5)
C
4 5
0.840.2
C
5 5
0.85
0.7373
（3） P(C ) 1 P(C) 1 P5( 5)
1
C
5 5
n重贝努利（Bernoulli ）试验的例子 1.已知在指定时间内某十字路口的事故率为p，现在此 时间段内对经过的n 辆机动车进行观察 每辆车是否经过这个十字路口是相互独立的，而且观
察结果有且只有这是一个贝努利试验
2.某射手每次射击命中目标的概率都是 p，现对同一目 标独立射击 n 次，观察射击结果 此射手独立射击n次，每次射击命中目标的概率都 是p，所以这n次射击构成独立试验序列，每次射击
比如 s 3, a 1, b 1 则再赌3局必分胜负
P{甲赢} P{X 2} P{X 2} P{X 3}
C32
(1)2 2
1 2
C33
( 1 )3 2
1 2
又如 s 3, a 1, b 2
则再赌2局必分胜负
P{甲赢}
P{X
2} C22
( 1 )2 2
1 4
第一章 小 结
设事件A：10件中至少有两件次品，则
10
p( A) p10 (k) 1 p10 (0) p10 (1) k 2 1 0.9610 C110 0.04 0.969 0.0582
（2）设事件B：前 9 次中抽到 8 件正品一件次品； 事件C：第 10 次抽到次品，则所求概率为
P(BC) P(B)P(C)
0.1 0.4 0.7
英文版概率论与数理统计重点单词
概率论与数理统计Probability Theory and Mathematical Statistics第一章概率论的基本概念Chapter 1 Introduction of Probability Theory不确定性indeterminacy必然现象certain phenomenon随机现象random phenomenon试验experiment结果outcome频率数frequency number样本空间sample space出现次数frequency of occurrencen维样本空间n-dimensional sample space样本空间的点point in sample space随机事件random event / random occurrence基本事件elementary event必然事件certain event不可能事件impossible event等可能事件equally likely event事件运算律operational rules of events事件的包含implication of events并事件union events交事件intersection events互不相容事件、互斥事件mutually exclusive exvents / /incompatible events互逆的mutually inverse加法定理addition theorem古典概率classical probability古典概率模型classical probabilistic model 几何概率geometric probability乘法定理product theorem概率乘法multiplication of probabilities条件概率conditional probability全概率公式、全概率定理formula of total probability贝叶斯公式、逆概率公式Bayes formula后验概率posterior probability先验概率prior probability独立事件independent event独立随机事件independent random event独立实验independent experiment两两独立pairwise independent两两独立事件pairwise independent events第二章随机变量及其分布Chapter 2 Random Variables and Distributions随机变量random variables离散随机变量discrete random variables概率分布律law of probability distribution一维概率分布one-dimension probability distribution 概率分布probability distribution两点分布two-point distribution伯努利分布Bernoulli distribution二项分布/伯努利分布Binomial distribution超几何分布hypergeometric distribution三项分布trinomial distribution多项分布polynomial distribution泊松分布Poisson distribution泊松参数Poisson theorem分布函数distribution function概率分布函数probability density function连续随机变量continuous random variable概率论与数理统计中的英文单词和短语概率密度probability density概率密度函数probability density function 概率曲线probability curve均匀分布uniform distribution指数分布exponential distribution指数分布密度函数exponential distribution density function正态分布、高斯分布normal distribution标准正态分布standard normal distribution正态概率密度函数normal probability density function正态概率曲线normal probability curve标准正态曲线standard normal curve柯西分布Cauchy distribution分布密度density of distribution第三章多维随机变量及其分布Chapter 3 Multivariate Random Variables and Distributions二维随机变量two-dimensional random variable联合分布函数joint distribution function二维离散型随机变量two-dimensional discrete random variable二维连续型随机变量two-dimensional continuous random variable联合概率密度joint probability variablen维随机变量n-dimensional random variablen维分布函数n-dimensional distribution functionn维概率分布n-dimensional probability distribution 边缘分布marginal distribution边缘分布函数marginal distribution function边缘分布律law of marginal distribution边缘概率密度marginal probability density二维正态分布two-dimensional normal distribution二维正态概率密two-dimensional normal probability 度density二维正态概率曲线two-dimensional normal probabilitycurve条件分布conditional distribution条件分布律law of conditional distribution条件概率分布conditional probability distribution条件概率密度conditional probability density边缘密度marginal density独立随机变量independent random variables第四章随机变量的数字特征Chapter 4 Numerical Characteristics fo Random Variables数学期望、均值mathematical expectation期望值expectation value方差variance标准差standard deviation随机变量的方差variance of random variables均方差mean square deviation相关关系dependence relation相关系数correlation coefficient协方差covariance协方差矩阵covariance matrix切比雪夫不等式Chebyshev inequality第五章大数定律及中心极限定理Chapter 5 Law of Large Numbers and Central Limit Theorem大数定律law of great numbers切比雪夫定理的special form of Chebyshev theorem特殊形式依概率收敛convergence in probability伯努利大数定律Bernoulli law of large numbers同分布same distribution列维-林德伯格定理、独立同分布中心极限定理independent Levy-Lindberg theorem辛钦大数定律Khinchine law of large numbers利亚普诺夫定理Liapunov theorem棣莫弗-拉普拉斯定理De Moivre-Laplace theorem第六章样本及抽样分布Chapter 6 Samples and Sampling Distributions统计量statistic总体population个体individual样本sample容量capacity统计分析statistical analysis统计分布statistical distribution统计总体statistical ensemble随机抽样stochastic sampling / random sampling 随机样本random sample简单随机抽样simple random sampling简单随机样本simple random sample经验分布函数empirical distribution function样本均值sample average / sample mean样本方差sample variance样本标准差sample standard deviation标准误差standard error样本k阶矩sample moment of order k样本中心矩sample central moment样本值sample value样本大小、样本容量sample size样本统计量sampling statistics随机抽样分布random sampling distribution抽样分布、样本分布sampling distribution自由度degree of freedomZ分布Z-distributionU分布U-distribution第七章参数估计Chapter 7 Parameter Estimations统计推断statistical inference参数估计parameter estimation分布参数parameter of distribution参数统计推断parametric statistical inference点估计point estimate / point estimation总体中心距population central moment总体相关系数population correlation coefficient总体分布population covariance总体协方差population covariance点估计量point estimator估计量estimator无偏估计unbiased estimate / unbiasedestimation估计量的有效性efficiency of estimator矩法估计moment estimation总体均值population mean总体矩population moment总体k阶矩population moment of order k总体参数population parameter极大似然估计maximum likelihood estimation极大似然估计量maximum likelihood estimator极大似然法maximum likelihood method /maximum-likelihood method似然方程likelihood equation似然函数likelihood function区间估计interval estimation置信区间confidence interval置信水平confidence level置信系数confidence coefficient单侧置信区间one-sided confidence interval置信上限confidence upper limit置信下限confidence lower limitU估计U-estimator正态总体normal population总体方差的估计estimation of population variance 置信度degree of confidence方差比variance ratio第八章假设检验Chapter 8 Hypothesis Testings参数假设parametric hypothesis假设检验hypothesis testing两类错误two types of errors统计假设statistical hypothesis统计假设检验statistical hypothesis testing检验统计量test statistics显著性检验test of significance统计显著性statistical significanceone-sided test单边检验、单侧检验one-sided hypothesis单侧假设、单边假设双侧假设two-sided hypothesis双侧检验two-sided testing显著水平significant levelrejection region拒绝域/否定区域接受区域acceptance regionU检验U-testF检验F-test方差齐性的检验homogeneity test for variances 拟合优度检验test of goodness of fit。
概率论与统计学基本知识chapt2english
Dot Plot
30
35
40
45
Stem-and-Leaf Display 茎叶图
Stem-and-leaf display combines graphic technique and sorting technique. It is very popular for summarizing numerical data.
1. Bar graph shows the amount of data that belongs to each class as proportionally sized rectangular areas
2. Pie chart shows the amount of data that belongs to each class as a proportional part of a circle
The researchers want to determine whether one type of aphasia occurs more often than any other, and, if so, how often.
Describing Qualitative data
Qualitative data are nonnumerical in nature, thus the value of a qualitative variable can only be classified into categories called classes. We can summarise such data numerically in two ways: (1) by counting
MPG
Histogram
概率论与数理统计-大学课件-ch1.1
随机试验
研究随机现象，首先要对研究对象进行观察试验. 这里的试验，指的是随机试验：.
如果每次试验的可能结果不止一个，且事先不能肯定 会出现哪一个结果，这样的试验称为随机试验.
例如, 掷寿硬命币试试验验 测命掷试. 一在枚掷同硬一一币颗工，骰艺观子掷条察，骰件出观子下正察试生还出验产是现出反的的.点灯数泡的寿
.
A B
AB
在可列无穷的场合，用 表示事件“A1、A2 、 …诸事件
同时发生。”
事件A发生但事件B不发生, 称为事件A与B的差事件。
A B
A B
显然：
AB
数理学院
SCHOOL OF MATHEMATICS AND PHYSICS
则称A和B是互不相容的或互斥的,
指事件A与B不可能同时发生。 基本事件是两两互不相容的。
H
T
随机试验的特点
数理学院
SCHOOL OF MATHEMATICS AND PHYSICS
试验可以在相同条件重复进行；
试验的可能结果不只有一个， 但试验的全部可能结果，是在试验前就明确的；
每次试验的结果是不可预知的.
数理学院
SCHOOL OF MATHEMATICS AND PHYSICS
样本空间与事件
数理学院
SCHOOL OF MATHEMATICS AND PHYSICS
表示事件A与事件B同时发生, 称为事件A与事件B
的积（交）事件，记为AB。积事件AB是由A与B的公共样本
点所构成的集合。
n个事件A1 , A2 , … , An 的积
记为A1 ∩ A2 ∩ … ∩ An ，
或A1A2 … An ，也可简记为
概率与统计课件第一章
Throwing a die
Chevalier De Mere
Blaise Pascal
Pierre de Fermat
Classical probability古典概率
Suppose a game has n equally likely outcomes, of which m outcomes The correspondence between Pascal and Fermat
changed only when an error has been made; negotiation is not appropriate
• Any questions?
Origins
• Let’s date back to 1650’s in France
• Gambling was fashionable
• Assignments submitted by a studying group（作业）25%
• A study group consists of up to 3 students, and they will receive the same grade on each submission of their homework
tools • To think in a probabilistic and statistical way
Contents to be covered
Probability
Distribution
Joint
分布
Dist.
Discrete random variables
Continuous random variables
• Course project （课程项目）15% (written report + oral presentation)
概率论与数理统计英语
概率论与数理统计英语English: Probability theory and mathematical statistics are two branches of mathematics that deal with the concepts and tools used to understand randomness and uncertainty in various phenomena. Probability theory is concerned with quantifying uncertainty and making predictions about the likelihood of certain events occurring, while mathematical statistics uses probability theory to draw conclusions about populations based on sample data. These two fields are closely related and often used together in applications such as insurance, finance, engineering, and social sciences. Probability theory involves concepts such as random variables, probability distributions, and the laws of large numbers, while mathematical statistics covers topics such as estimation, hypothesis testing, and regression analysis. Together, they provide a framework for understanding uncertainty and making informed decisions in the face of incomplete information.中文翻译: 概率论和数理统计是数学的两个分支，涉及用于理解各种现象中的随机性和不确定性的概念和工具。
(完整word版)概率论与数理统计(英文)
3. Random Variables3.1 Definition of Random VariablesIn engineering or scientific problems, we are not only interested in the probability of events, but also interested in some variables depending on sample points. （定义在样本点上的变量）For example, we maybe interested in the life of bulbs produced by a certain company, or the weight of cows in a certain farm, etc. These ideas lead to the definition of random variables.1. random variable definitionHere are some examples.Example 3.1.1 A fair die is tossed. The number X shown is a random variable, it takes values in the set {1,2,6}.Example 3.1.2The life t of a bulb selected at random from bulbs produced by company A is a random variable, it takes values in the interval (0,) .Since the outcomes of a random experiment can not be predicted in advance, the exact value of a random variable can not be predicted before the experiment, we can only discuss the probability that it takes somevalue or the values in some subset of R.2. Distribution function Definition3.1.2 Let X be a random variable on the sample space S . Then the function()()F X P X x =≤. R x ∈is called the distribution function of XNote The distribution function ()F X is defined on real numbers, not on sample space.Example 3.1.3 Let X be the number we get from tossing a fair die. Then the distribution function of X is (Figure 3.1.1)0,1;(),1,1,2,,5;61, 6.if x n F x if n x n n if x <⎧⎪⎪=≤<+=⎨⎪≥⎪⎩Figure 3.1.1 The distribution function in Example 3.1.3 3. PropertiesThe distribution function ()F x of a random variable X has the following properties :(1) ()F x is non-decreasing.SolutionBy definition,1(2000)(2000)10.6321P X F e -≤==-=.(10003000)(3000)(1000)P X P X P X <≤=≤-≤1.50.5(3000)(1000)(1)(1)0.3834F F e e --=-=---= Question ： What are the probabilities (2000)P X < and (2000)P X =? SolutionLet 1X be the total number shown, then the events 1{}X k = contains 1k - sample points, 2,3,4,5k =. Thus11()36k P X k -==, 2,3,4,5k = And512{1}{}k X X k ==-==so 525(1)()18k P X P X k ==-===∑ 13(1)1(1)18P X P X ==-=-=Thus0,1;5()(),11;181, 1.x F x P X x x x <-⎧⎪⎪=≤=-≤<⎨⎪≥⎪⎩Figure 3.1.2 The distribution function in Example 3.1.5The distribution function of random variables is a connection between probability and calculus. By means of distribution function, the main tools in calculus, such as series, integrals are used to solve probability and statistics problems.3.2 Discrete Random Variables 离散型随机变量In this book, we study two kinds of random variables. ,,}n aAssume a discrete random variable X takes values from the set 12{,,,}n X a a a =. Let()n n P X a p ==,1,2,.n = (3.2.1) Then we have 0n p ≥, 1,2,,n = 1n n p=∑.the probability distribution of the discrete random variable X (概率分布)注意随机变量X 的分布所满足的条件(1) P i ≥0(2) P 1+P 2+…+P n =1离散型分布函数And the distribution function of X is given by()()n n a xF x P X x p ≤=≤=∑ (3.2.2)Solutionn=3, p=1/2X p r01/813/823/831/8two-point distribution(两点分布)某学生参加考试得5分的概率是p, X表示他首次得5分的考试次数，求X的分布。
概率论与统计学的基本原理
概率论与统计学的基本原理概率论与统计学是数学中的两个重要分支，它们在各个领域的研究中起到了至关重要的作用。
概率论研究的是随机事件的发生规律，而统计学则通过对数据的分析和推理，从中得出有关总体特征的结论。
本文将介绍概率论与统计学的基本原理，包括概率的定义与性质、统计学的基本概念和方法等。
一、概率论的基本原理1. 概率的定义概率是描述随机事件发生可能性大小的一种数学工具。
在概率论中，将一个随机事件A的概率表示为P(A)，其取值范围在0到1之间。
当P(A)等于0时，表示事件A不可能发生；当P(A)等于1时，表示事件A一定会发生；当0<P(A)<1时，表示事件A以一定的概率发生。
2. 概率的性质概率具有以下几个基本性质：加法法则、乘法法则、互斥事件的概率、独立事件的概率等。
加法法则指示了对两个事件进行并运算时的概率计算方法，乘法法则则描述了对两个事件进行交运算时的概率计算方法。
互斥事件是指两个事件不可能同时发生，其概率计算方法为两个事件的概率之和。
独立事件是指两个事件的发生不会相互影响，其概率计算方法为两个事件的概率之积。
二、统计学的基本原理1. 总体与样本在统计学中，研究对象可以分为总体和样本。
总体是指研究者想要了解的整体，样本则是从总体中抽取的一部分个体。
通过对样本的研究和分析，可以得出有关总体的结论，这是统计学的基本思想。
2. 统计量统计量是样本的某个特征的函数，可以通过对样本数据进行计算得到。
常用的统计量有平均数、方差、标准差等。
平均数是样本的所有观测值之和除以观测值的总数，用于表示样本的集中趋势。
方差则用于表示样本的离散程度，标准差是方差的平方根。
3. 抽样分布抽样分布是指当样本容量趋近于无穷大时，样本统计量的分布情况。
常见的抽样分布有正态分布、t分布、F分布等。
这些分布是统计学中常用的工具，可以用来进行参数估计和假设检验等。
三、概率论与统计学的应用概率论和统计学在各个领域都有广泛的应用。
概率论与统计学的基本原理
概率论与统计学的基本原理概率论与统计学是数学中的重要分支，研究了事件发生的可能性以及从样本数据中得出结论的方法。
它们在各个领域中都有广泛的应用，包括工程、医学、金融和社会科学等。
本文将介绍概率论与统计学的基本原理，包括概率、随机变量、概率分布、假设检验等内容，旨在帮助读者了解这一重要学科的核心概念和方法。
1. 概率概率是描述事件发生可能性的数学工具。
概率的取值范围在0到1之间，其中0表示事件不可能发生，1表示事件一定会发生。
概率可以通过频率或者理论计算来确定。
频率方法是通过实验或观察事件发生的次数来计算，理论方法则是基于已知信息和假设进行计算。
2. 随机变量随机变量是概率论中的重要概念，表示随机试验的结果。
随机变量可以分为离散型和连续型两种类型。
离散型随机变量的取值为有限个或可数个，例如投掷一枚骰子的点数；而连续型随机变量的取值可以是整个数轴上的任意数值，例如身高、体重等。
3. 概率分布概率分布描述了随机变量的取值与相应概率之间的关系。
对于离散型随机变量，概率分布可以用概率质量函数（Probability Mass Function，简称PMF）表示；对于连续型随机变量，概率分布可以用概率密度函数（Probability Density Function，简称PDF）表示。
常见的概率分布包括二项分布、正态分布、泊松分布等，它们在实际问题中具有广泛的应用。
4. 统计推断统计推断是根据样本数据对总体特征进行推断的方法。
统计推断可以分为参数估计和假设检验两个方面。
参数估计用于估计总体的未知参数，例如通过样本数据估计总体均值、方差等。
假设检验则用于根据样本数据判断总体参数的假设是否成立，例如根据样本判断平均数是否显著不同于某个特定值。
5. 相关与回归分析相关与回归分析是统计学中研究变量间关系的方法。
相关分析用于衡量两个变量之间的线性相关程度，可通过计算相关系数来度量相关性的强度。
回归分析则用于建立一个或多个自变量与因变量之间的关系模型，并用该模型进行预测和解释。
概率论与统计学原理chapt3english
Solutions
Denote A: the customer uses mustard B: the customer uses ketchup P(A) = 0.75, P(B) = 0.80, P(A ∩ B) = 0.65. (a) P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.75 + 0.80 - 0.65 = 0.90. (b) D: the customer does not use any one of these two. D = (A ∪ B)C P(D) = 1 - P(A ∪ B) = 1 - 0.90 =0.10.
Probability rules for sample points
1. Probability of each sample point must lie between 0 and 1. 2. The probabilities of all the sample points within a sample space must sum to 1.
The additive rule and mutually exclusive events互斥事件
How to calculate the probability of A union B?
Additive rule of probability
Let A and B be two events in a sample space S. The probability of the union A and B is P(A ∪ B) = P(A) + P(B) - P(A ∩ B). 两个互斥事件的和的概率等于它们的概率之和
概率论与统计原理
《概率论与统计原理》课程期末复习资料《概率论与统计原理》课程讲稿章节目录：第一章事件的概率§1.1 随机事件和样本空间1.1.1 随机现象与随机试验1.1.2 随机事件1.1.3 样本空间§1.2 事件的关系和运算1.2.1 事件的关系和运算1.2.2 事件与集合的关系1.2.3 事件的运算性质§1.3 随机事件的概率1.3.1 概率的统计定义1.3.2 古典型概率1.3.3 几何型概率§1.4 概率的公理化定义1.4.1 概率的三条公理（概率的公理化定义）1.4.2 概率的性质§1.5 条件概率和事件的独立性1.5.1 条件概率1.5.2 乘法公式1.5.3 全概率公式1.5.4 贝叶斯公式1.5.5 事件的独立性第二章随机变量及其分布§2.1 随机变量及其分布函数2.1.1 随机变量2.1.2 随机变量的分布函数§2.2 离散型随机变量2.2.1离散型随机变量及其分布2.2.2 常用离散型概率分布§2.3 连续型随机变量2.3.1 连续型随机变量的定义2.3.2 常用连续型概率分布§2.4 随机变量函数的分布2.4.1 离散型随机变量函数的分布2.4.2 连续型随机变量函数的分布§2.5 多维随机变量简介2.5.1 多维随机变量的定义2.5.2 二维随机变量的联合分布函数2.5.3 边缘分布函数2.5.4 随机变量的独立性第三章随机变量的数字特征§3.1 随机变量的数学期望3.1.1 数学期望的定义3.1.2 随机变量函数的数学期望3.1.3 数学期望的性质§3.2 随机变量的方差3.2.1 方差和标准差的定义3.2.2 方差的性质3.2.3 切比雪夫不等式§3.3 常用分布的数学期望和方差3.3.1 常用离散型分布的数学期望和方差3.3.2 常见连续型分布的数学期望和方差§3.4 随机变量的矩第四章极限定理§4.1 大数定律4.1.1随机变量列的极限4.1.2 大数定律§4.2 中心极限定理4.2.1 列维-林德伯格定理4.2.2 棣莫佛-拉普拉斯（De Moivre-Laplace）定理第五章统计原理§5.1 数理统计的基本概念5.1.1 总体和样本5.1.2 统计量5.1.3 经验分布函数§5.2 抽样分布5.2.1 χ2分布5.2.2 t分布5.2.3 正态总体的抽样分布§5.3 参数估计5.3.1 统计估计的概念5.3.2 参数的点估计5.3.3 正态总体参数的区间估计§5.4 假设检验5.4.1 一个总体均值的假设检验5.4.2 一个正态总体方差σ2的假设检验5.4.3 一个总体比率的假设检验（大样本）一、客观部分：（单项选择）★考核知识点: 事件的关系和运算考核知识点解释：“事件A与事件B至少有一个发生”的事件，称为事件A与事件B的和（或并），记作A∪B或A+B。
概率与统计英语
概率与统计英语《概率论与数理统计》基本名词中英文对比表英文中文 Probability theory 概率论mathematical statistics 数理统计deterministic phenomenon 确定性现象random phenomenon 随机现象sample space 样本空间random occurrence 随机大事fundamental event 基本领件certain event 必定大事impossible event 不行能大事random test 随机实验incompatible events 互不相容大事frequency 频率classical probabilistic model 古典概型geometric probability 几何概率conditional probability 条件概率multiplication theorem 乘法定理Bayes's formula 贝叶斯公式Prior probability 先验概率Posterior probability 后验概率Independent events 互相自立大事Bernoulli trials 贝努利实验random variable 随机变量probability distribution 概率分布distribution function 分布函数discrete random variable 离散随机变量distribution law 分布律hypergeometric distribution 超几何分布random sampling model 随机抽样模型binomial distribution 二项分布Poisson distribution 泊松分布geometric distribution 几何分布probability density 概率密度continuous random variable 延续随机变量uniformly distribution 匀称分布exponential distribution 指数分布numerical character 数字特征mathematical expectation 数学期望variance 方差moment 矩central moment XXX矩n-dimensional random variable n-维随机变量two-dimensional random variable 二维离散随机变量joint probability distribution 联合概率分布joint distribution law 联合分布律joint distribution function 联合分布函数boundary distribution law 边缘分布律boundary distribution function 边缘分布函数exponential distribution 二维指数分布continuous random variable 二维延续随机变量joint probability density 联合概率密度boundary probability density 边缘概率密度conditional distribution 条件分布conditional distribution law 条件分布律conditional probability density 条件概率密度covariance 协方差dependency coefficient 相关系数normal distribution 正态分布limit theorem 极限定理standard normal distribution 标准正态分布logarithmic normal distribution 对数正态分布covariance matrix 协方差矩阵central limit theorem XXX极限定理Chebyshev's inequality 切比雪夫不等式Bernoulli's law of large numbers 贝努利大数定律statistics 统计量simple random sample 容易随机样本sample distribution function 样本分布函数sample mean 样本均值sample variance 样本方差sample standard deviation 样本标准差sample covariance 样本协方差sample correlation coefficient 样本相关系数order statistics 挨次统计量sample median 样本中位数sample fractiles 样本极差sampling distribution 抽样分布parameter estimation 参数估量estimator 估量量estimate value 估量值unbiased estimator 无偏估量unbiassedness 无偏性biased error 偏差mean square error 均方误差relative efficient 相对有效性minimum variance 最小方差asymptotic unbiased estimator 渐近无偏估量量uniformly estimator 全都性估量量moment method of estimation 矩法估量maximum likelihood method of estimation 极大似然估量法likelihood function 似然函数maximum likelihood estimator 极大似然估量值interval estimation 区间估量hypothesis testing 假设检验statistical hypothesis 统计假设simple hypothesis 容易假设composite hypothesis 复合假设rejection region 否决域acceptance domain 接受域test statistics 检验统计量linear regression analysis 线性回归分析1 概率论与数理统计词汇英汉对比表Aabsolute value 肯定值accept 接受acceptable region 接受域additivity 可加性adjusted 调节的alternative hypothesis 对立假设analysis 分析analysis of covariance 协方差分析analysis of variance 方差分析arithmetic mean 算术平均值association 相关性assumption 假设assumption checking 假设检验availability 有效度average 均值Bbalanced 平衡的band 带宽bar chart 条形图beta-distribution 贝塔分布between groups 组间的bias 偏倚binomial distribution 二项分布binomial test 二项检验Ccalculate 计算case 个案category 类别center of gravity 重心central tendency XXX趋势chi-square distribution 卡方分布chi-square test 卡方检验classify 分类cluster analysis 聚类分析coefficient 系数coefficient of correlation 相关系数collinearity 共线性column 列compare 比较comparison 对比components 构成，重量compound 复合的confidence interval 置信区间consistency 全都性constant 常数continuous variable 延续变量control charts 控制图correlation 相关covariance 协方差covariance matrix 协方差矩阵critical point 临界点critical value 临界值crosstab 列联表cubic 三次的，立方的cubic term 三次项cumulative distribution function 累加分布函数curve estimation 曲线估量Ddata 数据default 默认的definition 定义deleted residual 剔除残差density function 密度函数dependent variable 因变量description 描述design of experiment 实验设计deviations 差异df.(degree of freedom) 自由度diagnostic 诊断dimension 维discrete variable 离散变量discriminant function 判别函数discriminatory analysis 判别分析distance 距离distribution 分布D-optimal design D-优化设计Eeaqual 相等effects of interaction 交互效应efficiency 有效性eigenvalue 特征值equal size 等含量equation 方程error 误差estimate 估量estimation of parameters 参数估量estimations 估量量evaluate 衡量exact value 精确值expectation 期望expected value 期望值exponential 指数的exponential distributon 指数分布extreme value 极值 Ffactor 因素，因子factor analysis 因子分析factor score 因子得分factorial designs 析因设计factorial experiment 析因实验fit 拟合fitted line 拟合线fitted value 拟合值fixed model 固定模型fixed variable 固定变量fractional factorial design 部分析因设计frequency 频数F-test F检验full factorial design 彻低析因设计function 函数Ggamma distribution 伽玛分布geometric mean 几何均值group 组Hharmomic mean 调和均值heterogeneity 不齐性histogram 直方图homogeneity 齐性homogeneity of variance 方差齐性hypothesis 假设hypothesis test 假设检验Iindependence 自立independent variable 自变量independent-samples 自立样本index 指数index of correlation 相关指数interaction 交互作用interclass correlation 组内相关interval estimate 区间估量intraclass correlation 组间相关inverse 倒数的iterate 迭代Kkernal 核Kolmogorov-Smirnov test柯尔莫哥洛夫-斯米诺夫检验kurtosis 峰度Llarge sample problem 大样本问题layer 层least-significant difference 最小显著差数least-square estimation 最小二乘估量least-square method 最小二乘法level 水平level of significance 显著性水平leverage value XXX化杠杆值life 寿命life test 寿命实验likelihood function 似然函数likelihood ratio test 似然比检验 linear 线性的linear estimator 线性估量linear model 线性模型linear regression 线性回归linear relation 线性关系linear term 线性项logarithmic 对数的logarithms 对数logistic 规律的lost function 损失函数Mmain effect 主效应matrix 矩阵maximum 最大值maximum likelihood estimation 极大似然估量mean squared deviation(MSD) 均方差mean sum of square 均方和measure 衡量media 中位数M-estimator M估量minimum 最小值missing values 缺失值mixed model 混合模型mode 众数model 模型Monte Carle method 蒙特卡罗法moving average 移动平均值multicollinearity 多元共线性multiple comparison 多重比较multiple correlation 多重相关multiple correlation coefficient 复相关系数multiple correlation coefficient 多元相关系数multiple regression analysis 多元回归分析multiple regression equation 多元回归方程multiple response 多响应multivariate analysis 多元分析Nnegative relationship 负相关nonadditively 不行加性nonlinear 非线性nonlinear regression 非线性回归noparametric tests 非参数检验normal distribution 正态分布null hypothesis 零假设number of cases 个案数Oone-sample 单样本one-tailed test 单侧检验one-way ANOVA 单向方差分析one-way classification 单向分类optimal 优化的optimum allocation 最优配制order 排序order statistics 次序统计量origin 原点orthogonal 正交的outliers 异样值Ppaired observations 成对观测数据paired-sample 成对样本parameter 参数parameter estimation 参数估量partial correlation 偏相关partial correlation coefficient 偏相关系数partial regression coefficient 偏回归系数percent 百分数percentiles 百分位数pie chart 饼图point estimate 点估量poisson distribution 泊松分布polynomial curve 多项式曲线polynomial regression 多项式回归polynomials 多项式positive relationship 正相关power 幂P-P plot P-P概率图predict 预测predicted value 预测值prediction intervals 预测区间principal component analysis 主成分分析proability 概率probability density function 概率密度函数probit analysis 概率分析proportion 比例Qqadratic 二次的Q-Q plot Q-Q概率图quadratic term 二次项quality control 质量控制quantitative 数量的，度量的quartiles 四分位数Rrandom 随机的random number 随机数random number 随机数random sampling 随机取样random seed 随机数种子random variable 随机变量randomization 随机化range 极差rank 秩rank correlation 秩相关rank statistic 秩统计量regression analysis 回归分析regression coefficient 回归系数regression line 回归线reject 否决rejection region 否决域relationship 关系reliability 牢靠性repeated 重复的report 报告，报表residual 残差residual sum of squares 剩余平方和response 响应risk function 风险函数robustness 稳健性root mean square 标准差row 行run 游程run test 游程检验Ssample 样本sample size 样本容量sample space 样本空间sampling 取样sampling inspection 抽样检验scatter chart 散点图S-curve S形曲线separately 单独地sets 集合sign test 符号检验significance 显著性significance level 显著性水平significance testing 显著性检验significant 显著的，有效的significant digits 有效数字skewed distribution 偏态分布skewness 偏度small sample problem 小样本问题smooth 平滑sort 排序soruces of variation 方差来源space 空间spread 扩展square 平方standard deviation 标准离差standard error of mean 均值的标准误差standardization 标准化standardize 标准化statistic 统计量statistical quality control 统计质量控制std. residual 标准残差stepwise regression analysis 逐步回归stimulus 刺激strong assumption 强假设stud. deleted residual 同学化剔除残差stud. residual 同学化残差subsamples 次级样本sufficient statistic 充分统计量sum 和sum of squares 平方和summary 概括，综述Ttable 表t-distribution t分布test 检验test criterion 检验判据test for linearity 线性检验test of goodness of fit 拟合优度检验test of homogeneity 齐性检验test of independence 自立性检验test rules 检验法则test statistics 检验统计量testing function 检验函数time series 时光序列tolerance limits 容许限total 总共，和transformation 转换treatment 处理trimmed mean 截尾均值true value 真值t-test t检验two-tailed test 双侧检验Uunbalanced 不平衡的unbiased estimation 无偏估量unbiasedness 无偏性uniform distribution 匀称分布Vvalue of estimator 估量值variable 变量variance 方差variance components 方差重量variance ratio 方差比various 不同的vector 向量Wweight 加权，权重weighted average 加权平均值within groups 组内的ZZ score Z分数。
(完整版)概率论与数理统计英文版总结,推荐文档
x
F (x) P( X x) f (t)dt , (4.1.1)
The empty set, denoted by , is also an event, called an impossible event, means that it never
occurs in the experiment.
Probability of events （概率）
If the number of successes in n trails is denoted by s , and if the sequence of relative frequencies s / n obtained for larger and larger value of n approaches a limit, then this limit is defined as the
certain event（必然事件）：
The sample space S itself, is certainly an event, which is called a certain event, means that it
always occurs in the experiment.
impossible event（不可能事件）：
X12 3 4 …k …
P p q1p q2p q3p
qk－1 …
p
Binomial distribution（二项分布）
概率论与数理统计课件(完整版)
1. 计算相互独立的积事件的概率： 若已知n个事件A1, A2, …, An相互独立，则 P(A1A2…An)=P(A1)P(A2)…P(An)
系统一:先串联后并联
A1
B1
A2
B2
A3
B3
A4
B4
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例3. 100件乐器,验收方案是从中任 取3件测试(相互独立的), 3件测试后都认为音色纯则接收这批 乐器,测试情况如下: 经测试认为音色纯 认为音色不纯 乐器音色纯 0.99 0.01 乐器音色不纯 0.05 0.95
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1. 公式法：
当A＝S时, P(B｜S)=P(B), 条件概率化为无条件概率, 因此无条件概率可看成条件概率.
注
计算条件概率有两种方法:
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2.缩减样本空间法：
在A发生的前提下, 确定B的缩减样本空间, 并在其中计算B发生的概率, 从而得到P(B|A). 例2. 在1, 2, 3, 4, 5这5个数码中, 每次取一个数码, 取后不放回, 连取两次, 求在第1次取到偶数的条件下, 第2次取到奇数的概率.
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随机试验: (1) 可在相同的条件下重复试验; (2) 每次试验的结果不止一个,且能事先明确所有可能的结果; (3) 一次试验前不能确定会出现哪个结果.
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2. 样本空间与随机事件
样本空间的分类:
离散样本空间:样本点为有限个或可列个. 例 E1,E2等. 无穷样本空间:样本点在区间或区域内取值. 例 灯泡的寿命{t|t≥0}.
空集φ不包含任何样本点, 它在每次试验中都不发生，称为不可能事件。
概率论与数理统计书ppt课件
条件概率与独立性
CHAPTER
随机变量及其分布
02
随机变量的概念与性质
定义随机变量为在样本空间中的实值函数，其取值依赖于随机试验的结果。
随机变量
讨论随机变量的可数性、可加性、正态性等性质。
随机变量的性质
离散型随机变量的概念
定义离散型随机变量为只能取可数个值的随机变量。
离散型随机变量的分布
讨论离散型随机变量的概率分布，如二项分布、泊松分布等。
应用
中心极限定理及其应用
CHAPTER
贝叶斯推断与决策分析
07
贝叶斯推断的基本原理
金融风险管理
贝叶斯推断在金融风险管理领域有着广泛的应用，如信用风险评估、投资组合优化等。
医疗诊断
贝叶斯推断在医疗诊断方面也有着重要的应用，如疾病诊断、预后评估等。
机器学习与人工智能
贝叶斯推断在机器学习算法和人工智能领域中也有着广泛的应用，如朴素贝叶斯分类器、高斯混合模型等。
参数估计与置信区间
01
点估计
用单一的数值估计参数的值。
02
区间估计
给出参数的一个估计区间，通常包括一个置信水平。
比较两个或多个组的均值差异，确定因素对结果的影响。
方差分析
检验两个或多个组的方差是否相等。
方差齐性检验
研究变量之间的关系，并预测结果。
回归分析
假设检验与方差分析
CHAPTER
回归分析与线性模型
应用
在现实生活中，大数定律被广泛应用于保险、赌博、金融等领域，通过统计数据来预测未来的趋势和风险。
大数定律及其应用
在独立随机变量序列中，它们的和的分布近似于正态分布，即中心极限定理。这意味着，当样本量足够大时，样本均值近似于正态分布。
英文版概率论与数理统计重点单词
概率论与数理统计Probability Theory and Mathematical Statistics第一章概率论的基本概念Chapter 1 Introduction of Probability Theory不确定性indeterminacy必然现象certain phenomenon随机现象random phenomenon试验experiment结果outcome频率数frequency number样本空间sample space出现次数frequency of occurrencen维样本空间n-dimensional sample space样本空间的点point in sample space随机事件random event / random occurrence 基本事件elementary event必然事件certain event不可能事件impossible event等可能事件equally likely event事件运算律operational rules of events事件的包含implication of events并事件union events交事件intersection events互不相容事件、互斥事件mutually exclusive exvents / /incompatible events互逆的mutually inverse加法定理addition theorem古典概率classical probability古典概率模型classical probabilistic model 几何概率geometric probability 乘法定理product theorem概率乘法multiplication of probabilities条件概率conditional probability全概率公式、全概率定理formula of total probability贝叶斯公式、逆概率公式Bayes formula后验概率posterior probability先验概率prior probability独立事件independent event独立随机事件independent random event独立实验independent experiment两两独立pairwise independent两两独立事件pairwise independent events第二章随机变量及其分布Chapter 2 Random Variables and Distributions随机变量random variables离散随机变量discrete random variables概率分布律law of probability distribution一维概率分布one-dimension probability distribution 概率分布probability distribution两点分布two-point distribution伯努利分布Bernoulli distribution二项分布/伯努利分布Binomial distribution超几何分布hypergeometric distribution三项分布trinomial distribution多项分布polynomial distribution泊松分布Poisson distribution泊松参数Poisson theorem分布函数distribution function概率分布函数probability density function连续随机变量continuous random variable概率密度probability density概率论与数理统计中的英文单词和短语概率密度函数probability density function 概率曲线probability curve均匀分布uniform distribution指数分布exponential distribution指数分布密度函数exponential distribution density function正态分布、高斯分布normal distribution标准正态分布standard normal distribution正态概率密度函数normal probability density function正态概率曲线normal probability curve标准正态曲线standard normal curve柯西分布Cauchy distribution分布密度density of distribution第三章多维随机变量及其分布Chapter 3 Multivariate Random Variables and Distributions二维随机变量two-dimensional random variable联合分布函数joint distribution function二维离散型随机变量two-dimensional discrete random variable二维连续型随机变量two-dimensional continuous random variable联合概率密度joint probability variablen维随机变量n-dimensional random variablen维分布函数n-dimensional distribution function n维概率分布n-dimensional probability distribution 边缘分布marginal distribution边缘分布函数marginal distribution function边缘分布律law of marginal distribution边缘概率密度marginal probability density二维正态分布two-dimensional normal distribution二维正态概率密度two-dimensional normal probabilitydensity二维正态概率曲线two-dimensional normal probabilitycurve条件分布conditional distribution条件分布律law of conditional distribution条件概率分布conditional probability distribution条件概率密度conditional probability density边缘密度marginal density独立随机变量independent random variables第四章随机变量的数字特征Chapter 4 Numerical Characteristics foRandom Variables数学期望、均值mathematical expectation期望值expectation value方差variance标准差standard deviation随机变量的方差variance of random variables均方差mean square deviation相关关系dependence relation相关系数correlation coefficient协方差covariance协方差矩阵covariance matrix切比雪夫不等式Chebyshev inequality第五章大数定律及中心极限定理Chapter 5 Law of Large Numbers andCentral Limit Theorem大数定律law of great numbers切比雪夫定理的特殊形式special form of Chebyshev theorem依概率收敛convergence in probability伯努利大数定律Bernoulli law of large numbers同分布same distribution列维-林德伯格定理、独立同分布中心极限定理independent Levy-Lindberg theorem辛钦大数定律Khinchine law of large numbers利亚普诺夫定理Liapunov theorem棣莫弗-拉普拉斯定理De Moivre-Laplace theorem第六章样本及抽样分布Chapter 6 Samples and Sampling Distributions 统计量statistic总体population个体individual样本sample容量capacity统计分析statistical analysis统计分布statistical distribution统计总体statistical ensemble随机抽样stochastic sampling / random sampling 随机样本random sample简单随机抽样simple random sampling简单随机样本simple random sample经验分布函数empirical distribution function样本均值sample average / sample mean样本方差sample variance样本标准差sample standard deviation标准误差standard error样本k阶矩sample moment of order k样本中心矩sample central moment样本值sample value样本大小、样本容量sample size样本统计量sampling statistics 随机抽样分布random sampling distribution抽样分布、样本分布sampling distribution自由度degree of freedomZ分布Z-distributionU分布U-distribution第七章参数估计Chapter 7 Parameter Estimations统计推断statistical inference参数估计parameter estimation分布参数parameter of distribution参数统计推断parametric statistical inference点估计point estimate / point estimation总体中心距population central moment总体相关系数population correlation coefficient总体分布population covariance总体协方差population covariance点估计量point estimator估计量estimator无偏估计unbiased estimate / unbiasedestimation估计量的有效性efficiency of estimator矩法估计moment estimation总体均值population mean总体矩population moment总体k阶矩population moment of order k总体参数population parameter极大似然估计maximum likelihood estimation极大似然估计量maximum likelihood estimator极大似然法maximum likelihood method /maximum-likelihood method似然方程likelihood equation似然函数likelihood function区间估计interval estimation置信区间confidence interval置信水平confidence level置信系数confidence coefficient单侧置信区间one-sided confidence interval置信上限confidence upper limit置信下限confidence lower limitU估计U-estimator正态总体normal population总体方差的估计estimation of population variance 置信度degree of confidence方差比variance ratio第八章假设检验Chapter 8 Hypothesis Testings参数假设parametric hypothesis假设检验hypothesis testing两类错误two types of errors统计假设statistical hypothesis统计假设检验statistical hypothesis testing检验统计量test statistics显著性检验test of significance统计显著性statistical significance单边检验、单侧one-sided test检验单侧假设、单边one-sided hypothesis假设双侧假设two-sided hypothesis双侧检验two-sided testing显著水平significant level拒绝域/否定区rejection region域接受区域acceptance regionU检验U-testF检验F-test方差齐性的检验homogeneity test for variances 拟合优度检验test of goodness of fit。
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Survey
With a survey, the researchers sample a group of people, ask questions and record the responses. They collect information systematically and directly from respondents Survey methods: telephone surveys, mail surveys, internet survey, computer interviews, door-to-door personal interviews, and mall intercept studies.
Collecting Data
Generally, we can obtain data in four different ways: 1. Data from a published source 2. Data from a designed experiment 3. Data from a survey 4. Data from an observational观察 study.
Fundamental elements of statistics
4. A sample样本 is a subset of the units of a 样本 population. 5. A statistical inference统计推断 is an estimate, 统计推断 testing, prediction, or same other generalization about a population based on information contained in a sample.
Quantitative data
DEF 1.9 Quantitative data are measurements that are recorded on a naturally occurring numerical scale. The responses to questions such as “How old are you?” or "How tall are you?" are clearly numerical.
PROBABILITY & STATISTICS
Lecturer: Yu Yu Office: 8412 Email: yuyu@
Course Outline
1. Descriptive Statistics: [Chapters 1 & 2] 2. Probability: [Chapters 3 – 5] 3. Inferential Statistics I: [Chapters 6 – 7]
Learning Objectives
1. Define Statistics 2. Distinguish Descriptive & Inferential statistics 3. Define Population, Sample, Variable, Parameter, & Statistic 4. Distinguish Quantitative & Qualitative data 5. Four types of collecting data
Fundamental elements of statistics
7. Statistic统计量 is a numerical characteristic 统计量 of a sample. The “average” of 500 MSNBC news viewers. The value of a statistic can be calculated after a sample to be collected.
Qualitative data
DEF 1.10 Qualitative data are measurement that cannot be measured on a natural numerical scale; they can only be classified into one of a group of categories. For example, the response to the question ‘which subject is your first choice?’ is categorical. The choices are clearly ‘International Finance’, ‘Economics’, ‘Marketing’ …, or ‘Statistics’.
A planned activity whose results yield a set of data. In a designed experiment, researchers control strictly over the units (people, objects, or things). This includes both the activities for selecting the units and obtaining the data values. Most of laboratory results are obtained in designed experiment.
1. Involves
Estimation Hypothesis Testing
Population?
2. Purpose
Make Decisions About Population Characteristics
Fundamental elements of statistics
1. Population总体 is a collection or set of units (usually 总体 people, objects, transactions, or events) that we are interested in studying. 2. An experimental unit试验单位 is an object (e.g., 试验单位 person, object, transaction, or event) upon which we collect data. 3. A variable变量 is a characteristic or property of 变量 interest about each individual population or sample unit.
Types of Data
Data is a set of values (numbers, words, or symbols) collected for the variable from each of the units belonging to the sample or population. Two types of data: qualitative data quantitative data.
Example
According to USA Today, (Dec. 19, 1999), the average age of viewers of MSNBC cable television news programming is 50 years. Suppose a rival network executive hypothesizes that the average age of MSNBC viewers is less than 50. To test her hypothesis, she samples 500 MSNBC news viewers and collects the age of each. Describe the population. Describe the variable of interest. Describe the sample. Describe the inference推论.
Types of Statistical Applications
The field of statistics can be roughly subdivided into two areas: 1. descriptive statistics 描述型 2. inferential statistics 推论型
Reliability可靠性
Since we use the information contained in the smaller sample to learn about the larger population and so we can not be certain that an inference about a population is correct. We need to know how good the inference is – its reliability (or risk), i.e. how to measure the uncertainty in inferences. DEF 1.8A measure of reliability is a statement (usually quantified) about the degree of uncertainty associated with a statistical inference. The measure of reliability shows the dialectical thinking. It also separates the science of statistics from the art of fortune-telling.
Course Grading