RANDOM PATHS ORIGINATING WITHIN A CONVEX REGION AND TERMINATING ON ITS SURFACE

A ray is defined as a straight line originating within an arbitrary convex body K in n -dimensional Euclidean space and terminating on the surface of K. The distributions of ray length are derived for three types of randomness. The results are expressed as functions of the overlap volume and overlap surface content of K with its translated self.     

Understanding Risk Management

Discussions of technological risks and their management by corporations and society are ubiquitous and often acrimonious. Equally ubiquitous are several important misconceptions of key risk questions. This paper (i) argues that serious epistemological confusion pervades much of the scientific basis for risk assessment, especially confusion among objective, subjective, and perceived risk, and between facts and ethical values; and (ii) asserts that this confusion combines with psychological aspects of risk perception to produce a confused risk debate, a societal management of risks often based on diffuse or contradictory objectives, and consequently mismanagement of resource allocation to risk reduction.     

A probabilistic model for table tennis

A probabilistic model for table tennis is derived and probabilities of winning and expected durations are presented for a game and for a match. A simpler model, ignoring the effects of service, is compared with the complete model.     

Comparison of Confidence Procedures for Type I Censored Exponential Lifetimes

In the model of type I censored exponential lifetimes, coverage probabilities are compared for a number of confidence interval constructions proposed in literature. The coverage probabilities are calculated exactly for sample sizes up to 50 and for different degrees of censoring and different degrees of intended confidence. If not only a fair two-sided coverage is desired, but also fair one-sided coverage's, only few methods are quite satisfactory. A likelihood-based interval and a third root transformation to normality work almost perfectly, but the ²-based method that is perfect under no censoring and under type II censoring can also be advocated.     

信用风险模型比较分析

本文分析了现代信用风险模型迅速发展的主要原因,对主要派别的代表性模型用数学语言进行了总结,比较分析了各模型的原理及优缺点,并简要介绍了各模型的实证效果。     

On The Quantitative Definition of Risk

A quantitative definition of risk is suggested in terms of the idea of a "set of triplets". The definition is extended to include uncertainty and completeness, and the use of Bayes' theorem is described in this connection. The definition is used to discuss the notions of "relative risk", "relativity of risk", and "acceptability of risk".     

A Decision Theory Perspective on the Disposal of High-Level Radioactive Waste

In this paper the problem of high-level nuclear waste disposal is viewed as a five-stage, cascaded decision problem. The first four of these decisions having essentially been made, the work of recent years has been focused on the fifth stage, which concerns specifics of the repository design. The probabilistic performance assessment (PPA) work is viewed as the outcome prediction for this stage, and the site characterization work as the information gathering option. This brief examination of the proposed Yucca Mountain repository through a decision analysis framework resulted in three conclusions: (1) A decision theory approach to the process of selecting and characterizing Yucca Mountain would enhance public understanding of the issues and solutions to high-level waste management; (2) engineered systems are an attractive alternative to offset uncertainties in the containment capability of the natural setting and should receive greater emphasis in the design of the repository; and (3) a strategy of waste management should be adopted, as opposed to waste disposal, as it allows for incremental confirmation and confidence building of a permanent solution to the high-level waste problem.     

The search for submarine pingos in the Beaufort Sea: An unusual application of the binomial distribution

Almost all statistical estimation problems involving the binomial distribution occur with the number of independent Bernoulli trials, n, being a known parameter and the probability of success, p, being unknown. Applications in which n is unknown and p is known are extremely rare. One such application to a real problem in the physical sciences is the subject of this note.     

遵循心理学规律搞好工科数学教学

通过对概率统计的多年教学实践经验的总结,探讨了在教学过程中如何遵循心理学规律,激发学生的学习兴趣,培养学生的良好学习习惯和创新能力.指出要改革以教师为中心"满堂灌"的传统教学模式;利用好"启发式"和"讨论式"教学方法,培养学生的学习兴趣和求知欲;改革考试模式,利用好考试这个指挥棒,正确引导学生的学习目的,使他们端正学习态度,避免学生仅仅为应付考试而学习的现象.     

略论民事诉讼中的证明标准

本文探讨了民事诉讼中证明标准与证明要求的区别,认为我国民事诉讼法过去所实行的证明标准存在诸多弊端,应当从立法上确立"高度盖然性"之标准,并进行相关制度的改革。