二项分布

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。

Through the research of binomial probability distribution function,it has been proved that the PDF is a monotone increasing function of probability p and allowable failure time r in test,and is a monotone decreasing function of test time n.

通过对二项分布函数的研究，证明它是关于概率p和试验中允许失败次数r的单调增函数，是关于试验次数n的单调减函数。

Model of stochastic interest rate was established by reflected Brownian motion and negative binomial distribution. Based on the stochastic interest rate model, the combined life insurance was discussed.

bstract 以反射布朗运动和负二项分布为基础建立随机利率模型，并在该随机利率模型下对联合生命保险进行讨论。

A model of stochastic interest rate was established by reflected Brownian motion and negative binomial distribution. Based on the stochastic interest rate model, the combined life insurance was discussed.

以反射布朗运动和负二项分布为基础建立随机利率模型，并在该随机利率模型下对联合生命保险进行讨论。

Besides, how to improve sequential test is discussed.Then, the data structure design of reliability block diagram and assessment algorithms of system reliability software is discussed, the method how to resolve the key problems is given, the functions of the software and how to use is introduced, too.

同时，以二项分布为例，讨论了序贯检验方法的改进然后，讨论了武器系统可靠性评估软件的可靠性框图数据结构设计和评估算法实现，给出了关键问题的解决办法，简要介绍了软件的功能与使用。

By applying the theory of infinite series, this paper proves a factorial inequality and proposes an improved upper bound of the parameter on Stirling s formula.

应用级数理论证明了一个关于阶乘的不等式，从而给出Stirling公式中参数的一个改进上界，并在此基础上，对一个有关产品检测的古典概率———二项分布的近似计算问题进行了讨论

Based on analysis on index of gathering, Cnidocampa flavescens hibernating cocoon is defined to be in negative binominal distribution.

通过聚集度指标的计算分析，明确了黄刺蛾越冬茧呈聚集型的一般负二项分布。

The testing, answering system was developed out by the ASP.net. Two test papers were abstracted from the system by the combination of the certain proportion and binominal distribution mathematical models stragety. The two test papers were tested by 52 students through the cross design. The difficulty and discrimination of items and the reliability and validity of the test papers were worked out with Education Statistics, factor analysis, relative analysis etc.

运用ASP.net技术开发了组卷、答卷、阅卷系统，应用重点等级定额比例分配与难度等级二项分布数学模型相结合的组卷策略随机抽出2套试卷，采用交叉设计对52名预防医学本科学生进行测试，用教育测量学原理、因子分析、相关性分析等方法分析两套试卷试题的难度、区分度和试卷的信度、效度。

Cronbach a of them equals respectively 1.000, 0.714. Conclusions The system could form the test pater with the strategy of the combination of the certain proportion of the important degree and the binominal distribution models which realized the Internet testing, rectifying and analysis.The test papers abstracted from the system were reliable and valid. It can scientificly, objectively evaluate the students' ability and it's beneficial to deviation of the teaching, testing and controlling testing cheat. The Non-paper testing system has good practical value.

建立的试题库和考试系统能够按重点等级定额比例分配与难度等级二项分布模型策略组卷，实现了远程考试、自动阅卷和相关分析功能；从该系统抽取的试题难度和区分度合适，试卷可信、有效；能够客观、公正、科学地测试和评价学生的能力，对开展教考分离、控制考试作弊起到积极作用，具有较好的实用价值。

With these conclusions,we present an accurate algorithm to solve the simultaneous inequality of binomial PDF.An optimum solution can be worked out by adopting multivariate half-folded searching algorithm,so that we can get the sampling plan of testability demonstration accurately and quickly.

根据这些结论，提出了求解二项分布的联立不等式的精确算法，在可能的求解区域采用多变量折半搜索的算法，确定联立不等式的最优解，从而可以快速准确地获得测试性验证的抽样方案。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。