数学期望

The traditional mathematical expectation also results in the problem which puzzled the economist many years such as the Allais paradox and the Ellesberg paradox ...

Choquet(1953)提出了容度的概念以后，Choquet积分作为对传统数学期望的一种改进，被自然的引如到经济学中来。

In a certain period, the probability and expected value of critical drought duration got larger with the in crease of first-order auto-correlation coefficient and skewed coefficient, especially with first-order autocorrelation coefficient. The return periods of consecutive 11-year drought in North Luo River and Jing River were 1000 years.

在一定时期内，极限水文干旱历时的发生概率和数学期望随一阶自相关系数、偏态系数的增加而增大，且一阶自相关系数对极限水文干旱历时概率分布影响较为显著；泾河和洛河发生连续11年干旱的重现期均为1000年。

Events,Operation and Relation of Sets, Classical Probability, Geometrical Probability , Statistical Stability of a Frequency, Axioms of Probability, Conditional Probability, Total Probability Theorem, Bayes' Rule,Independent Events,Independent Repeated Trials, One Dimensional Random Variables, Discrete Random Variables, Distribution Function of a Random Variables , Continuous Random Variables, Normal Distribution, Distribution of a Function of a Random Variable, Multidimensional Random Variables, Joint Distribution Function, Marginal Distribution Function,Discrete Two—Dimensional Random Variables,Continuous Two—Dimensional Random Variables, Independent Random Variables, Distribution of Functions of Random Variables,Expectation,Variance, Covariance, Coefficient of Correlation, Bivariate Normal Distribution, Law of Large Numbers, The Central Limit Theorems, Sample and Population ,Chi—Squared, T and F Distributions , Sampling Distributions , Point Estimation , Interval Estimation , Testing Hypotheses , A Test of Significance for Parameters in a Single Sample From a Normally Distributed Population , A Test of Significance for Parameters in Two Sample From Normally Distributed Populations .

本课程的主要内容：概率的概念与运算、随机变量及其分布、随机变量的数字特征与极限定理、数理统计的基本概念、估计和检验的基本方法，随机事件与概率随机事件、事件的关系与运算、几何概率、统计概率等，条件概率、全概率公式、贝叶斯公式、事件的独立性、二项概率公式，随机变量的概念、离散型随机变量、随机变量的分布函数、连续型随机变量、随机变量函数的分布，多维随机变量及其分布函数、边缘分布函数、随机变量的独立性、二维随机变量函数的分布，数学期望、方差、协方差和相关系数、大数定律、中心极限定理，总体与样本， X 2-分布、 t-分布和 F-分布，统计量及抽样分布，假设检验的基本概念、单个正态总体参数的显著性检验、两个正态总体参数的显著性检验。

Some fundamental properties of fuzzy probability characteristic, such as the fuzzy mean value function, fuzzy covariance function and fuzzy variance function of fuzzy stochastic processes are proved.

3研究了实模糊随机变量的数学期望、方差等模糊概率特征的基本性质以及计算方法，并且讨论了实模糊随机变量的独立性与分析运算的若干基本性质

Mathematical expectation is the random variable one of the important features of mathematics, the average value of random variable response to the size, in practical application has a pivotal role.

数学期望是随机变量的重要数学特征之一，它反映随机变量平均取值的大小，在实际应用中有着举足轻重的作用。

Based on the limited mathematical expectation, the density function, distribution function and other mathematical tools, the impact of the use of different types of deductible and compensation limit on the pure premiums is analysed.

在有限数学期望、密度函数、分布函数等数学工具的基础上，分析了不同类型的免赔额与赔偿限额的同时使用，对纯保费的影响。

This paper, the future market conditions as a random event, according to the probability of higher mathematics in the theory of the future market and the level of information, analysis and evaluation of mathematical expectation of random variable as a random variable reflects the average level, it is important to the probability of random variable characteristics.

本文把未来市场状况作为随机事件，依据高等数学中的概率理论，对未来市场和信息的水平作出分析和评价，由于随机变量的数学期望体现了随机变量的平均水平，它是随机变量的重要概率特征。

Based on the the limited mathematical expectation, the density function and other mathematical tools,we analyze the impact of the use of different types of deductible and compensation limit on the pure premiums. It has great significance for the insurance and actuarial staff to design more rational and more fair insurance types.

并在有限数学期望、密度函数、分布函数等数学工具的基础上，分析了不同类型的免赔额与赔偿限额的同时使用对纯保费的影响，对保险精算人员设计出加更加合理、更加公平的保险险种有很大的意义。

The stochastic programming becomes a common programming after the expectation is gotten. An algorithm is given to solve this kind of programming.

在求得模型中各随机变量的数学期望之后，将随机规划问题转化为通常的数学规划问题，并给出了求解这类问题的一个算法。

This paper introduced the appliance of probability and statistics in reality,including classical model,formula of total probability, normal distribute,mathematics expectation and the central limit theorem.While it also discusses the widely uses of probability and statistics and the close relationship with the real life.Therefore,it lays the theoretical foundation for the practical uses with probability and statistics,and the basis of mathematics model.

本文介绍了概率统计的某些知识在实际问题中的应用，主要围绕古典概型，全概率公式，正态分布，数学期望，极限定理等有关知识，探讨概率统计知识在实际生活中的广泛应用，进一步揭示概率统计与实际生活的密切联系，为应用概率知识解决实际问题，数学模型的建立，学科知识的迁移奠定一定的理论基础。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。