理论概率

In this paper the method of combinational mathematics is used to deduce the probability generation function of the longest run in the Bernoulli trials,and get the probability generation function without using its probability function of kth order geometric distribution.

游程及其相关理论广泛地应用于随机检验、质量控制、DNA数据分析等许多领域，提出使用组合数学的方法推导出贝努利试验中最长游程的概率发生函数的计算公式，利用所得到的结果可以不用k阶几何分布的概率函数而很容易地得出它的概率发生函数。

In this paper the event tree is used in the analysis on cascading failures and by use of probability approximation theory of rare event the probability order of multiple failures is divided, thus the screening process of multiple failures can be simplified.

文章采用事件树对连锁故障的分析方法，运用小概率事件的概率近似理论对多重故障进行概率阶次划分，可以简化多重故障的筛选过程。

In the proposed frame of theory, probability density function or distribution function are also involved, but their standing are secondary. Probability density function is treated only as a probabilistic features of the failure rate function.

在本文倡导的理论体系中，也要涉及概率密度函数或分布函数，但他们仅被视为失效率函数的概率特征，讨论的路线是失效率函数的模式如何决定寿命分布的概率性质。

Based on the theory of probability statistic, a non-fixed value probability finite element analysis method by using FEA software ANSYS and Monte Carlo method was studied, by which the probability characteristic of projectile strength failure function was analyzed.

本文以概率统计为理论基础，综合采用有限元分析法和蒙特卡罗法，拟对弹体强度失效概率特征的非确定性概率有限元分析方法进行探讨。

The papes utilizer Parzen's kernel estimate theory which was used in estimating the function ofprobability intensity and Chen Xiru's results in the field to strictly prove the following fact.Whenusing non-completeness knowledge sample W to find the law which W would be kept to,thefrom:is closer to real pthan the estimate of rectangular diagram.

本文借鉴Parzen提出的概率密度函数的核估计理论和陈希孺教授等研究的结论，用概率论的方法严格证明了下列事实：用非完备知识样本估计其观测值应遵循的概率分布规律时，扩散型估计：得到的分布比用直方图法得到的估计更接近于真实概率分布p。

This course explores the history and debates over codifying the laws of probability, how probability theory applies to specific cognitive processes, how it relates to the human understanding of causality, and how new computational approaches to causal modeling provide a framework for understanding human probabilistic reasoning.

本课程探索关于概率法则形成的历史和争论，概率理论如何运用于具体的认知过程，它与人类对因果的理解有着怎样的关系，以及新的关于因果模型计算方法怎样为理解人类的概率推理过程提供了一个框架。

This course explores the history and debates over codifying the laws of probability, how probability theory applies to specific cognitive processes, how it relates to the human understanding of causality, and how new computational approaches to causal modeling provide a framework for understanding human probabilistic reasoning.

本课程探索关于概率法则形成的历史和争论，概率理论如何运用于具体的认知过程，它与人类对因果的理解有着怎样的关系，以及新的关于因果模型计算方法怎样为理解人类的概率推理过程提供了框架。

Monte Carlo is a method that approximately solves mathematic or physical problems by statistical sampling theory. When comes to Bayesian classification, it firstly gets the conditional probability distribution of the unlabelled classes based on the known prior probability. Then, it uses some kind of sampler to get the stochastic data that satisfy the distribution as noted just before one by one. At last, it can obtain the posterior probability distibution of each unlabelled classes by analysing these stochastic data.

蒙特卡罗是一种采用统计抽样理论近似求解数学或物理问题的方法，它在用于解决贝叶斯分类时，首先根据已知的先验概率获得各个类标号未知类的条件概率分布，然后利用某种抽样器，分别得到满足这些条件分布的随机数据，最后统计这些随机数据，就可以得到各个类标号未知类的后验概率分布。

Limit Theory is one of the branches and also an important theoretical basis of science of Probability and Statistics.

概率极限理论就是其主要分支之一，也是概率统计学科中极为重要的理论基础。

As stated in the classical book "Limit distributions for sums of independent random variables"(1949) by B.V.Gendenko and A.N.

概率极限理论就是其主要分支之一，也是概率统计学科中极为重要的理论基础。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷