查询词典 probability function

Then we introduced transition probability kernel for the hidden state process and the confederated process. In the deep research, we found that some similar parameters of state transition probability, observation symbol probability and initial state probability were involved in the transition probability kernel of the confederated process. So we can complete the training of traditional HMM parameters by training the transition probability kernel of the confederated process. To our surprised, we got the consistency of transition probability kernel of the confederated process. Meanwhile, we proved the rationality and reliability of the parameters estimation equations under the classical B-W algorithm.

然后对联合过程的转移概率核展开研究，我们根据过程的取值空间的不同，引入了隐状态空间和联合过程空间上的转移概率核，研究中发现在联合空间上的转移概率核包含了在一般的隐马氏模型的参数估计中的所有类似的三组参数(转移概率，观测概率和初始概率)，因此对传统的隐马氏模型的参数训练我们可以通过联合过程的转移概率核的训练来完成，更令我们惊奇的是联合过程的转移概率核还具有一致性；同时对于Baum提出的经典的B-W算法给出的关于模型的参数重估计公式，证明了它的合理性和可靠性，即模型经过重估计后的参数能够满足给定的单观测序列在模型下发生的概率是单调递增的。

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。

Chapter 1 we introduce the risk process with positive and negative risk sums,show the background of the risk process. Chapter 2 we show the integral and differential equation of birth probability,give the Lundberg inequation that the ruin probability satisfies with martingale approach,then discuss then ruin probability of the risk process with two dependent positive and negative risk sums,study how the dependence impacts on the ruin probability. Chapter 3 we compare the concrete examples by numbers,and makes further comparison between the two results coming out of independency and dependency,with the purpose of narrating their respective impacts on the probability of ruin probability.

本文第一章引入含正、负风险和的风险模型，介绍风险过程的实际背景；第二章给出生存概率Φ所满足的积分-微分方程，利用典型鞅方法给出破产概率Ψ满足的Lundberg不等式，并且讨论两个相关正、负风险和模型的破产概率，研究相关性对破产概率的影响；第三章对具体实例给出数值比较，进一步把相关性和独立性两种情形的结果进行比较，说明对破产概率的影响。

Based on probability theory, a method for describing and calculating the collision probability between rendezvous and docking vehicle and debris is presented, and the method involves quantitatively analyzing the collision probability using quasi maximum instantaneous collision probability and total collision probability. The method calculating the indexes is developed, and the input required to perform a calculation includes the respective state vectors, position error covariance matrices and physical sizes of objects involved.(3) Two methods to analyze relative trajectory safety between chaser and target are developed, which are 3-sigma ellipsoid based methodology and collision probability based methodology.

1分析了交会对接各阶段面临的主要轨迹安全威胁，阐述了被动和主动安全策略、目标器的交会对接控制区域等保证交会安全的措施；(2)基于概率思想发展了线性和非线性运动情况下飞行器与空间碎片的碰撞判断方法，提出采用总碰撞概率和拟最大瞬时碰撞概率来综合描述飞行器与空间碎片的碰撞危险程度，推导了通过飞行器和空间碎片各自的状态矢量、位置误差协方差矩阵以及形状尺寸来计算碰撞概率的公式；(3)提出了两种分析追踪器和目标器之间相对轨迹安全的新方法：基于3σ椭球的轨迹安全分析方法和基于碰撞概率的轨迹安全分析方法。

Firstly,the classification of probability rule is analyzed on the base of classic rough set concepts and extended to the equal relation of set in the indefinite system,namely,the upper and lower approximation space of research set is expressed in the form of conditional probability;then,according to the measure of probability rule,the attributes reduction is carried out and the classification rule is extracted by using the related parameters of condition attributes' impend precision from the angle of conditional probability;Finally,the related simulation test result is given and the result shows the classification rules with probability measures is more rational.

首先在经典粗糙集概念的基础上分析概率规则的分类，并将其推广到不确定系统的集合等价关系中，即用条件概率的形式表示研究集合的上下近似空间；然后根据概率规则的测度从条件概率的角度利用条件属性的逼近精度的相关参数进行属性集的约简进而提取分类规则；最后给出了相关的仿真实验结果，结果表明带有概率测度的分类规则更合理。

The output probability distribution of charge carrier multiplier structure from the electron multiplying charge-coupled device and its influence on image uniformity are studied. The probability model is established for the CCM structure of EMCCD. And based on the probability generating function and its properties, the probability distribution function of multiple CCM stages is deduced and its application in improving image uniformity is also discussed.

为了研究电子倍增电荷耦合器件中电荷载流子倍增结构的输出概率分布及其对图像均匀性的影响，建立了EMCCD中CCM结构的概率模型，利用概率生成函数推导了多级CCM倍增结构的输出概率密度函数，讨论了PDF在提高图像均匀性中的应用。

Based on the interval probability and the second fuzzy probability, go a step further the definition and characters of random variables with the third fuzzy probability and the fuzzy distribution function and fuzzy probability distribution sequence were put forward.,the definition and characters of mathematical expectation and variance were studied also.

在区间概率和第二类模糊概率的基础上，进一步给出了具有第三类模糊概率的随机变量及其模糊分布函数和模糊分布列的定义和性质，并研究了模糊概率随机变量的模糊数学期望和模糊方差的定义和性质，进一步完善了模糊概率理论。

Secondly, by establishing a discrete time Markov model with spatial reuse for a MANET, we analyze the performance of the network under the AODV routing protocol. The average route length and the probability to communicate within a limited hop distance are obtained. Several performance parameters of the route discovery and route maintain process are analytically studied, such as the probability generating function and the expectation of the flooding distabce. the probability that a route is discovered by a query packet with a "hop limit", the probability that a request packet finds a valid route, the average time needed to discover a valid route and the cost to successfully route a data packet to its destination. Furthermore, we present a concrete example based on the transmitter characteristic of directional antennas and obtain the corresponding results.

建立了移动自组网络空间可重用的离散时间马氏链模型，得到了AODV路由协议下网络任意两节点间的平均路由长度、在指定"跳限"要求下通信的概率；对随选型路由协议下路由发现和路由维护过程中若干网络性能参数进行了解析分析，如网络中任意两节点问的泛洪距离的概率母函数及其期望、限定泛洪步数时成功寻路的概率、发现一条有效路由的平均时间、成功路由的代价等；并基于定向天线的发射特征给出了一个具体实例，分析计算了相应的网络性能参数。

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。

After the joint probability density function between the 'float' ambiguity solution and the fixed ambiguity solution is introduced in this section, the conditional probability density function of the integer ambiguity solution is gotten according to this joint probability density function.

在介绍了模糊度浮点解和其固定解的联合概率密度函数之后，本文根据这个联合概率密度函数得到了模糊度整数解的条件概率密度函数。

Now he worked in ajoint venture.

现在他在一家合资企业工作。

More troops in Afghanistan won't change any of the foregoing.

更多的在阿富汗的军队也不会改变之前的状况。