英文版统计学_Chapter2
(完整word版)英文版概率论与数理统计重点单词
概率论与数理统计中的英文单词和短语概率论与数理统计Probability Theory and Mathematical Statistics第一章概率论的基本观点Chapter 1Introduction of Probability Theory不确立性indeterminacy必定现象certain phenomenon随机现象random phenomenon试验experiment结果outcome频次数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基本领件elementary event必定事件certain event不行能事件impossible event等可能事件equally likely event事件运算律operational rules of events事件的包括implication of events并事件union events交事件intersection events互不相容事件、mutually exclusive exvents/互斥事件/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formula of total probability概率定理贝叶斯公式、逆Bayes formula概率公式后验概率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散布Chapter2Random Variables and Distributions随机变量random variables失散随机变量discrete random variables概率散布律law of probability distribution一维概率散布one-dimension probability distribution 概率散布probability distribution两点散布two-point distribution伯努利散布Bernoulli distribution二项散布 / 伯努Binomial distribution利散布超几何散布hypergeometric distribution三项散布trinomial distribution多项散布polynomial distribution泊松散布Poisson distribution泊松参数Poisson theorem散布函数distribution function概率散布函数probability density function连续随机变量continuous random variable概率密度probability density概率密度函数probability density function概率曲线probability curve平均散布uniform distribution指数散布exponential distribution指数散布密度函exponential distribution density 数function正态散布、高斯normal distribution散布标准正态散布standard normal distribution正态概率密度函normal probability density function数正态概率曲线normal probability curve标准正态曲线standard normal curve柯西散布Cauchy distribution散布密度density of distribution第三章多维随机变量及其散布Chapter 3 Multivariate Random Variables and Distributions二维随机变量two-dimensional random variable结合散布函数joint distribution function二维失散型随机two-dimensional discrete random 变量variable二维连续型随机two-dimensional continuous random 变量variable结合概率密度joint probability variablen 维随机变量n-dimensional random variablen 维散布函数n-dimensional distribution functionn 维概率散布n-dimensional probability distribution边沿散布marginal distribution边沿散布函数marginal distribution function边沿散布律law of marginal distribution边沿概率密度marginal probability density二维正态散布two-dimensional normal distribution二维正态概率密two-dimensional normal probability 度density 二维正态概率曲two-dimensional normal probability 线curve条件散布conditional distribution条件散布律law of conditional distribution条件概率散布conditional probability distribution条件概率密度conditional probability density边沿密度marginal density独立随机变量independent random variables第四章随机变量的数字特点Chapter 4 Numerical Characteristics fo Random Variables数学希望、均值mathematical expectation希望值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有关关系dependence relation有关系数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制理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特别形式依概率收敛convergence in probability伯努利大数定律Bernoulli law of large numbers同散布same distribution列维 - 林德伯格independent Levy-Lindberg theorem定理、独立同分布中心极限制理辛钦大数定律Khinchine law of large numbers利亚普诺夫定理Liapunov theorem棣莫弗 - 拉普拉De Moivre-Laplace theorem斯定理第六章样本及抽样分布Chapter 6 Samples and Sampling Distributions统计量statistic整体population个体individual样本sample容量capacity统计剖析statistical analysis统计散布statistical distribution统计整体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经验散布函数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标准偏差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sample size容量样本统计量sampling statistics 随机抽样散布random sampling distribution抽样散布、样本sampling distribution散布自由度degree of freedomZ 散布Z-distributionU 散布U-distribution第七章参数预计Chapter 7Parameter Estimations统计推测statistical inference参数预计parameter estimation散布参数parameter of distribution参数统计推测parametric statistical inference点预计point estimate / point estimation整体中心距population central moment整体有关系数population correlation coefficient整体散布population covariance整体协方差population covariance点预计量point estimator预计量estimator无偏预计unbiased estimate/ unbiasedestimation预计量的有效性efficiency of estimator矩法预计moment estimation整体均值population mean整体矩population moment整体 k 阶矩population moment of order k整体参数population parameter极大似然预计maximum likelihood estimation极大似然预计量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区间预计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置信上限置信下限U 预计正态整体整体方差的预计confidence upper limit confidence lower limitU-estimatornormal populationestimation of population variance置信度方差比degree of confidence variance ratio第八章假定查验Chapter 8Hypothesis Testings参数假定假定查验两类错误统计假定统计假定查验查验统计量明显性查验统计明显性parametric hypothesis hypothesis testingtwo types of errors statistical hypothesis statistical hypothesis testing test statisticstest of significance statistical significance单边查验、单侧one-sided test查验单侧假定、单边one-sided hypothesis 假定两侧假定两侧查验明显水平拒绝域 / 否认区two-sided hypothesis two-sided testing significant level rejection region域接受地区acceptance regionU 查验F 查验方差齐性的查验拟合优度查验U-testF-testhomogeneity test for variances test of goodness of fit。
应用数理统计课件(配庄楚强版教材)第二章
（ξ1,ξ2,..,ξn), 则（ξ1,ξ2,…,ξn)的联合分布函
数为： F ( x1 , x2 ,L , xn )
= P { ξ1 < x1 , ξ 2 < x2 , ..., ξ n < xn }
= P { ξ1 < x1}P{ ξ 2 < x2 } ⋅ ... ⋅ P{ ξ n < xn }
（2）χ2 分布（Chi-square distribution）
χ 2 ～χ 2 (n)
{ } p分位点：χ p2 (n ) 满足P
χ
2
<
χ
2 p
(n)
=p
p53（9 347）表 4
χ
2 0.95
(9
)
=
16.91（9
p540)
表p 4 χ2 分布分位数表
n
p
8
9
0 ．90 13．362 14．684
又如：α = 0.1，uα = u0.1 = ? (表中没有)
u0.1 = −u1−0.1 = −u0.9 = −1.282
对称性(symmetricy)：
0.1
uα = −u1−α
α = 0.1
u0.1
u1− 0.1
习题或附表中α通常是指分位点之外的概率（面积）
单侧分位点：α放在分位点u1−α的一侧 双侧分位点: α分割放在正负对称的
2 +L +
)
m
1
9
二. t 分布 (t distribution)
Definition: 若ξ～N(0,1), η～χ2(n)且相互独立,
则有
t=
ξ η
～ t (n )
统计学要点摘要英文版-Statistic-Review
Chapter 2 Statistic ReviewA.Random variables;1.expected value:Define ：X is a discrete random variable，“ the mean （or expected value）of X " is the weighted average of the possible outcomes，where the probabilities of theoutcome serve as the appropriate weight。
p i is ith of prob。
, i=1，2，……nInterpretation: The random variable is a variable that have a probability associated with each outcome. Outcome is not controlled.Discrete random Var. ：has finite outcome，or outcome is countable infinite。
Continuous random Var。
: uncountable infinite outcome, the probability of each outcome is small because of too many numbers.For normal random Var.，probability density function is used to calculate the probability between the are。
E（)：the expectations operator,→… “ sample mean”, used to estimateThe is changed from sample to sample。
英文商务统计学ppt课件_Ch02
Tabulating Data
Graphing Data
Summary Table
Bar Charts
Pie Charts
Pareto Chart
Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc.
Banking Preference
16% 24% 2%
ATM Automated or live telephone Drive-through service at branch In person at branch Internet
17%
41%
Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc.
Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc.
Chap 2-5
Organizing Categorical Data: Bar Chart
In a bar chart, a bar shows each category, the length of which represents the amount, frequency or percentage of values falling into a category.
Chap 2-3
Organizing Categorical Data: Summary Table
A summary table indicates the frequency, amount, or percentage of items in a set of categories so that you can see differences between categories.
基础统计学简介(英文版)
1-5 5
Who Uses Statistics?
Statistical techniques are used extensively by managers in marketing, accounting, quality control, consumers, professional sports people, hospital administrators, educators, politicians, physicians, gamblers, etc...
1-9 9
Types of Statistics
– This is why younger people pay more for insurance…
• Knowledge of statistical methods at least helps you understand why decisions are made
– In future you will make decisions that involve data
1-6 6
Types of Statistics
Descriptive Statistics: Methods of organizing, summarizing, and presenting data in an informative way.
EXAMPLE 1: A Gallup poll found that 49% of the people in a survey knew the name of the first book of the Bible. The statistic 49 describes the number out of every 100 persons who knew the answerstics?
社会统计学02
Definition
❖ Frequency Distribution (or Frequency Table)
shows how a data set is partitioned among all of several categories (or classes) by listing all of the categories along with the number of data values in each of the categories.
two consecutive
lower class
boundarHale Waihona Puke es10Class
10
Width
10
10
10
10
14
Reasons for Constructing Frequency Distributions
1. Large data sets can be summarized. 2. We can analyze the nature of data. 3. We have a basis for constructing
90
4. Outliers: Sample values that lie 80
70
very far away from the vast
60
majority of other sample values. 50
East
40
West
5. Time: Changing characteristics 30
class width
(maximum value) – (minimum value) number of classes
统计学(中英文)_ch01
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 1-12
∑X
n
i
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 1-8
Inferential Statistics 推断统计
Estimation 估计 e.g., Estimate the population mean weight using the sample mean weight 例如：利用采样的平均重量估计人口的平均体 重 Hypothesis testing 假设检验 e.g., Test the claim that the population mean weight is 120 pounds 例如：根据测试的要求，人口平均体重是120 磅
英文翻译乃自己所做， 英文翻译乃自己所做，有错误 之处请自行查证。 之处请自行查证。
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 1-1
Business Statistics, A First Course
Defined descriptive vs. inferential statistics 描述性统计和推理统计 Reviewed data types 回顾数据类型
♦ ♦ ♦ ♦
Categorical vs. Numerical data 绝对的和数值的数据 Discrete vs. Continuous data 离散的和连续的数据
基础统计学英文版
Knowledge of statistical methods at least helps you understand why decisions are made
In future you will make decisions that involve data
Types of Statistics
❖ Descriptive Statistics: Methods of organizing, summarizing, and presenting data in an informative way.
EXAMPLE 2: According to Consumer Reports, General Electric washing machine owners reported 9 problems per 100 machines during 2002. The statistic 9 describes the number of problems out of every 100 machines.
Types of Statistics
❖ Descriptive Statistics: Methods of organizing, summarizing, and presenting data in an informative way.
EXAMPLE 1: A Gallup poll found that 49% of the people in a survey knew the name of the first book of the Bible. The statistic 49 describes the number out of every 100 persons who knew the answer.
统计学英文版教材课件
Combining Events
There are some important ways in which events can be combined that we will encounter repeatedly throughout this course. Suppose we have two events, A and B .
For example, A ∪ B = {1, 3, 4, 5}.
S A 1 5 2
STAT7055 - Lecture 2
B 3 4
6
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Introduction
Intersection, Union and Complement
Complement
STAT7055 - Lecture 2
February 17, 2016
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Introduction
Definitions
Probabilities of Outcomes
The probability of an outcome occurring on a single trial is written as P (Oi ). Probabilities associated with the outcomes in a sample space must satisfy two important requirements:
STAT7055 - Lecture 2
February 17, 2016
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Introduction
Events
Events
A simple event is an individual outcome from the sample space. An event is a collection of one or more simple events (or outcomes).
统计学课件(英文)
Descriptive vs. Inferential Statistics
Descriptive statistics: involves arranging, summarizing, and presenting a set of data in such a way that useful information is produced. Its methods make use of graphical techniques and numerical descriptive measures (such as averages) to summarize and present the data Inferential statistics: generalizing from a sample to a population, estimating unknown population parameters, drawing conclusions, making decisions.
ቤተ መጻሕፍቲ ባይዱ13
Scale of Measurement: Ratio
The data have the properties of interval data and the ratio of two values is meaningful. Contains a meaningful zero value that indicates that nothing exists for the variable at the zero point .
15
Kinds of Data (variables)
Qualitative (Categorical) data:
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2.1 - 15
Reasons for Constructing Frequency Distributions
1. Large data sets can be summarized. 2. We can analyze the nature of data.
3. We have a basis for constructing important graphs.
4. Using the first lower class limit and class width, proceed to list the other lower class limits. 5. List the lower class limits in a vertical column and proceed to enter the upper class limits. 6. Take each individual data value and put a tally mark in the appropriate class. Add the tally marks to get the frequency.
2.1 - 11
Upper Class Limits
are the largest numbers that can actually belong to different classes
Upper Class Limits
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3. Distribution: The nature or shape of the spread of data over the range of values (such as bell-shaped, uniform, or skewed).
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4. Outliers: Sample values that lie very far away from the vast majority of other sample values. 5. Time: Changing characteristics of the data over time.
Lecture Slides
Elementary Statistics Eleventh Edition
and the Triola Statistics Series
by Mario F. Triola
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2.1 - 3
Preview Important Characteristics of Data
1. Center: A representative or average value that indicates where the middle of the data set is located. 2. Variation: A measure of the amount that the data values vary.
Class Width
is the difference between two consecutive lower class limits or two consecutive lower class boundaries
10
Class Width
10 10 10 10 10
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Copyright © 2010 2010,Pearson 2007, 2004 Education Pearson Education, Inc. All Rights Reserved.
2.1 - 7
Pulse Rates of Females and Males
Original Data
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2.1 - 12
Class Boundaries
are the numbers used to separate classes, but without the gaps created by class limits
59.5 69.5 79.5 89.5 99.5
Class Boundaries
class width
(maximum value) – (minimum value) number of classes
3. Starting point: Choose the minimum data value or a convenient value below it as the first lower class limit.
2.1 - 5
Key Concept
When working with large data sets, it is often helpful to organize and summarize data by constructing a table called a frequency distribution, defined later. Because computer software and calculators can generate frequency distributions, the details of constructing them are not as important as what they tell us about data sets. It helps us understand the nature of the distribution of a data set.
2.1 - 8
Frequency Distribution Pulse Rates of Females
The frequency for a particular class is the number of original values that fall into that class.
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109.5
119.5 129.5
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2.1 - 13
Class Midpoints
are the values in the middle of the classes and can be found by adding the lower class limit to the upper class limit and dividing the sum by two
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2.1 - 16
Constructing A Frequency Distribution
1. Determine the number of classes (should be between 5 and 20). 2. Calculate the class width (round up).
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2.1 - 17
Relative Frequency Distribution
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2.1 - 6
Definition
Frequency Distribution (or Frequency Table)
64.5
74.5
Class Midpoints
84.5
94.5
104.5 114.5
124.5
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2.1 - 14
Section 2-2 Frequency Distributions
Copyright © 2010 Pearson Education Copyright © 2010 2010,Pearson 2007, 2004 Education Pearson Education, Inc. All quency Distributions
Definitions
Copyright © 2010 2010,Pearson 2007, 2004 Education Pearson Education, Inc. All Rights Reserved.