组合概率

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。

Through a probability problem,a connection is showed between binomial distribution and negative binomial distribution and therefore a composed formula is set up,which is proved by way of probability and algebra.

通过一个概率问题，给出二项分布与负二项分布的一种联系，从而建立一个组合公式，并由概率思维方式与代数方式给出证明

Based on the relationship between the risk-aversion coefficient and the confidence level in VaR, liquidity-adjusted VaR at any confidence level was obtained.

由于投资者风险偏好系数和VaR下的置信概率水平具有一一对应关系，可以通过最优路径集下执行成本的期望和标准差组合曲线来获得不同置信概率下，经过流动性调整后的VaR。

The research shows that asymmetry information can cause sluggish behaviour for the same type of employees, the exogenous layoff probability can restrain labour positivity and threaten the efficient labour of the employees, and reduce the agent cost. While endogenetic layoff probability cannot impact on the function of the assembled mechanisms consisting of promotion and fixed income under asymmetry information, which can avoid the moral risk of employees to achieve the same degree of their labour under symmetry information.

研究表明：非对称信息会诱导同类员工偷懒行为，外生裁员概率抑制员工的劳动积极性，对员工的有效劳动构成一种威胁，但裁员概率降低了代理成本；外生裁员机制并不影响信息非对称下的晋升激励和固定收入组合机制持有的避免员工道德风险的功能，实现员工对称信息下的努力程度；以绩效评估为特征的内生裁员机制能够促使异类员工更加努力工作，提高产量，相应地也增加了工资支出；高能员工比低能员工更努力，提高员工裁员绩效标准和高能员工比例，有利于降低代理成本。

The chapter 3 investigates the constructive method which means that many combinatorial numbers, such as Stirling number, Bell number, harmonic number, Fibonacci number and the number of derangement, are represented to moments of some random variables. This method is used in the computation of combinatorial sums, discovery and proof of combinatorial identities.

第三章研究了构造性概率方法，即一些常见组合变量(以后统称组合数为组合变量)的概率表示，诸如Stirling数、Bell数、调和数、Fibonacci数、错排数都可以表示为一些随机变量的矩，这些概率表示可以用来研究组合和式的计算与恒等式的证明。

If these parameters are determined, the uniqueness of evaluation result is contrary to the high risk of exploration. This paper analyzes the distribution characteristics of probability and the probability value by Montekaro simulation, all possibilities are simulated. And all possibilities can be gaine...

本文运用蒙特卡罗模拟进行风险分析，对勘探阶段的所有主要不确定因素的概率分布特征和概率值进行详细分析，力求不漏掉任何一种可能，通过蒙特卡罗模拟得出其所有可能值，最后运用这些模拟值和其他确定的参数进行勘探项目的经济评价，得出各种因素组合的经济评价结果和评价指标的概率分布值，量化了勘探参数和评价指标的风险。

Reduced SQP based on orthonormal bases, orthogonal bases and coordinate bases are studied and compared. With the correction item introduced, the null-space move is adjusted and the reduced SQP based on coordinate bases decomposition is improved.●The key problem of steady-state data processing for RTOPT is studied. A new algorithm of simultaneous strategies for data reconciliation and gross error detection is proposed. Here the objective function that is constructed using maximum likelihood principle and joint distribution function is minimized. Efficient algorithm is developed which exploited the nonlinear lease-square structure of this objective function.

仿真结果表明了算法的有效性；●深入研究了在线优化中的一个关键问题——稳态数据处理问题，用基于组合概率分布的目标函数联立求解粗劣误差检测和数据调和问题；以精馏塔在线优化的数据处理和模型修正为例，提出一种根据模型方程对参数的依赖性进行过程模型分解的分层策略，可以将数据调和和参数估计统一在数据处理的大框架中，为进一步的过程性能分析、操作状况评价以及在线优化提供可靠的基准，具有非常重要的工程应用价值；●将优化命题的形式扩展到更通用的形式。

Our results show that the rate of correlation among the random variables of those output sequences are low although they are not independent; in addition, the output sequences of those combined generators are homogeneous Markov chains which are strictly stationary processes with ergodicity; the output sequences of those combined generators are also proved to summit to the strong law of large numbers and the central limit theorem; finally the computation formula of the rate of the accordance between the output sequences and input sequences of those combined generators is given.

我们的研究结论表明：虽然这些序列中随机变量之间不具有相互独立性，但它们的相关程度却比较低；证明了"停走"生成器，KM_1M_2型组合生成器和加法型组合生成器的概率模型输出序列都是强平稳的和遍历的齐次马氏链；讨论了这些序列的概率极限性质，证明了它们均服从强大数定律和中心极限定理；还分别给出了各类生成器的输出序列与输入序列之间的符合率的计算公式。

Secondly, the properties of output sequences of stop-and-go clocked combiners are discussed. It is proved that the output sequences are stationary and obey strong law of large numbers and central limit theorem. Using the probabilistic model properly built, we analyze the rate of coincidence between the output sequences of two kinds of generators with basic operations and corresponding LFSRs sequences. All the computational formulae are derived. A recursive algorithm for efficiently computing the poster probability of partial input strings and corresponding joint probability is introduced. Moreover, divide-and-conquer attacks on this kind of generators which reconstruct the initial states of the input stop-and-go generators individually are proposed.

其次，分析了一般钟控停走组合生成器输出序列的概率分布性质，证明了生成器的输出序列是严平稳的，且服从强大数定律和中心极限定理；考察了钟控加法型组合生成器和钟控乘法型组合生成器的输出序列和相应的常规钟控下线性移位寄存器序列之间的符合率，给出了符合率的具体计算公式；给出了组合器输出序列段和输入序列段之间的联合分布以及部分输入序列段的后验概率的有效递归算法，进一步提出了利用后验概率对钟控组合生成器进行分别征服相关攻击的方法。

Cervus simulations demonstrated that the theoretical expectations for parentage exclusion of 10 microsatellite loci and six most polymorphic of the 10 loci were both 0.99, and the assignment success rate of the 6 most polymorphic microsatellite loci set was nearly to 0.97 with 95% confidence.

Cervus模拟分析表明从10个微卫星基因座组合中选取的多态性信息含量最高的6个进行组合与原组合的累积排除概率均在0.99，多态性信息含量最高的6个基因座的组合判定正确率为0.97，置信度为95%。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失