事件概率

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。

In order to make conditional inference,the expression of conditional events is discussed in this paper.

为了进行条件推理，本文讨论了条件事件的表示，并给出了相应的逻辑运算规则，引入了零事件间的概率比和多重条件事件的超条件事件概率的概念，它们均是无条件情形的推广。

The Six Sigma Black Belt should demonstrate a grasp of basic probability concepts, such as the probability of mutually exclusive events, of dependent and independent events, of events that can occur simultaneously, etc.

6西格玛黑带应掌握基础的概率概念，比如互斥事件的概率、关联和独立事件的概率、同时发生事件的概率等等。

Fast composite-event probability algorithm with both linear time and space complexity is proposed.

提出了一种可应用于电力系统充裕度分析的快速组合事件概率求取方法。

A mixed reasoning method is advised to deal with multifold fuzzy numbers of the probability of the event.

针对事件概率可取多种模糊数情况，提出了模糊因果图混合推理方法。

P×P and P were two major non-Bayesian algorithms. 6 Less than 25% of the participants used frequency. In those who got other results except P , much more people used probability. Experiment 2 had a randomized multigroup posttest design. There was only one factor named implied condition which had five levels: not imply, imply P, imply addition, imply division and imply all. The results showed that: 1 All the implied conditions significantly improved the participants' performance. When under the condition of implying division, the participants derived the best results. 2 31.9% of the participants got correct answer, 73% of who used frequency to rewrite the information. 3 78% of the participants could apply one or several of the four concepts: probability of "not the event", multiplication rule, addition rule and condition probability.

结果表明：1 被试的估计受问题内容的影响，权威型问题情境容易使被试高估，非权威型问题情境使被试的高估现象大大减少；数据结构和提问形式对被试估计不产生影响。2 有近5%的被试能正确估计P，其中 73%使用频数对信息进行再表征。3 贝叶斯推理中各分步骤的困难程度由低到高分别是：乘法、P、加法、除法。4 有50%的被试能运用对立事件概率、概率乘法、概率加法、条件概率这四个概念中的一种或者几种。5 使用最多的两种非贝叶斯算法是P×P和P。6 不到25%的被试使用频数；求得除P以外各类结果的被试中，使用概率的人数远多于使用频数的。

Discovering passage of event happened by tracing along terminal point of event on probability tree, utilizing multiplication formula and addition of probability again, the probability of an event may be caculated and some problems that students grasp with difficulty and make easily mistakes can be solved.

用概率树法求事件发生的概率，只需在概率树上沿事件的终点向前回溯，便可以发现事件发生的通道，再利用概率的乘法公式和概率的可加性，就解决了概率论中学生很难掌握的、容易出错的问题。

For this purpose, the safety state of the structure is regarded as a fuzzy set in the universe of discourse of the structural state, i.e. the safety event is considered as a fuzzy event and the mathematics model of the fuzzy event probability is adopted to be a unified model of the structural reliability analysis.

为此，本文将结构的安全状态看作是结构状态论域中的一个模糊集合，即认为安全事件为一模糊事件，采用模糊事件概率的数学模型作为结构可靠性分析的统一模型。

According to probability of"Mutex"" Appose "and"Reciprocity".

通过互斥事件、对立事件、相互独立事件概率的剖析，指出教师要注意一些容易混淆概念的教学。

As long as we grasp the theoretical explanation of these little probability event,we are able to explain their philosophical thoughts,get to know its real performance,scientifically sel...

只要我们掌握了小概率事件的理论解说，就可以诠释它的哲学思想，认识小概率事件的现实表现，科学地选择好的小概率事件，避开不好的小概率事件，以便趋利避害。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。