浅析全概率公式的应用

归蚋总结全概率公式的理解方法、求解问题的分析方法、解题步骤以及应用此公式时应注意的事项等几点教学体会，旨在使学生能够真正理解和掌握全概率公式，从而更好地解决这类实际问题。     

德布罗意公式不属于量子力学理论体系中的公式——兼与北师大梁绍荣先生商榷

论述了德布罗意公式不属于量子力学理论体系中的公式。指出梁绍荣等编的《量子力学》一书中,用德布罗意公式推导出自由粒子的波函数的错误。本文用量子力学理论推导出自由粒子的波函数。     

Sample size determinations when two binomial proportions are very small

Sample size determination for testing the hypothesis of equality of proportions with a specified type I and type I1 error probabilitiesis of ten based on normal approximation to the binomial distribution. When the proportionsinvolved are very small, the exact distribution of the test statistic may not follow the assumed distribution. Consequently, the sample size determined by the test statistic may not result in the sespecifiederror probabilities. In this paper the author proposes a square root formula and compares it with several existing sample size approximation methods. It is found that with small proportion (p≦.01) the squar eroot formula provides the closest approximation to the exact sample sizes which attain a specified type I and type II error probabilities. Thes quare root formula is simple inform and has the advantage that equal differencesare equally detectable.     

Option pricing for generalized distributions

The Black Scholes formula has been widely used to price financial instruments. The derivation of this formula is based on the assumption of lognormally distributed returns which is often in poor agreement with actual data. An option pricing formula based on the generalized beta of the second kind (GB2) is presented. This formula includes the Black Scholes formula as a special case and accommodates a wide variety of nonlognormally distributed returns. The sensitivity of option values to departures from the skewness and kurtosis associated with the lognormal distribution is investigated.     

Distribution of the sum of independent generalized logarithmic series variables

Jain and Gupta (1973) have given a generalized logarithmic series distribution which, for β = 1, reduces to the logarithmic series distribution. In this note we obtain the distribution of the sum of independent generalized logarithmic series variables. This distribution conforms, in a special case, to the First-type Stirling distribution (Patil and Wani, 1965) and would be useful in estimation theory.     

The Lindeberg-Feller theorem for positive definite densities

We consider the Lindeberg-Feller model for independent random variables and focus our attention on the behaviour of the probability densities q_{n} of sums S_{n}, n\geq 1 . We obtain a theorem on the convergence of q_{n} to the standard normal density \varphi which resembles the well known limit theorem for distribution functions--provided that the q_{n} are positive definite. A special case is the following: if q_{n}(0)\rightarrow\varphi(0) as n\rightarrow\infty then the Lindeberg condition guarantees that the convergence of q_{n} to \varphi continues to the real line.     

Breastfeeding and emerging motherhood identity: An interpretative phenomenological analysis of first time Chinese Australian mothers’ breastfeeding experiences

BackgroundChinese Australian mothers are more likely than the general Australian mothers to introduce formula in the first month of age. A better understanding of the context of formula introduction in the early weeks of birth can provide a deeper insight into how Chinese Australian mothers can be supported to continue exclusive breastfeeding.MethodsAn interpretative phenomenological analysis approach was used to examine the lived breastfeeding experiences of 11 first time Chinese mothers in Australia. The experiences of those who breastfed exclusively were compared to those who introduced formula in the first month after birth.FindingsAn overarching theme across all participants’ narratives was the meaning ascribed to breastfeeding in their emerging motherhood identity. Breastfeeding could be a pragmatic and a socially desirable method to nourish an infant but lacking personal identification to the mother. These mothers were more vulnerable to the early introduction of formula, especially when the support environment was lacking. Maternal identity conflict was common and negatively impacted exclusive breastfeeding and mothers’ mental health. In contrast, mothers who identified closely with breastfeeding showed greater persistence and enjoyment in breastfeeding and were more likely to continue breastfeeding exclusively. Health professionals were perceived to have an important influence in strengthening maternal breastfeeding motivation and self-efficacy.ConclusionBreastfeeding support to Chinese Australian mothers needs to consider how breastfeeding can be better integrated with their motherhood identity. Health professionals are well-positioned to facilitate this process through a better understanding of mothers’ cultural and social contexts around breastfeeding.     

中国共产党处理和解决民族问题的两大法宝

中国共产党根据马克思主义关于民族问题基本原理,坚持唯物的辨证的和历史的观点及方法揭示民族发展规律,结合中国的民族特点,提出我国处理和解决民族问题的基本政策:民族平等团结,民族区域自治,促进了民族地区社会、经济发展,促进了民族团结和共同繁荣,这是马克思主义民族理论与中国实际问题相结合的结晶,顺乎民意,合乎国情。     

Demystifying the Integrated Tail Probability Expectation Formula

ABSTRACT

Calculating the expected values of different types of random variables is a central topic in mathematical statistics. Targeted toward students and instructors in both introductory probability and statistics courses and graduate-level measure-theoretic probability courses, this pedagogical note casts light on a general expectation formula stated in terms of distribution and survival functions of random variables and discusses its educational merits. Often consigned to an end-of-chapter exercise in mathematical statistics textbooks with minimal discussion and presented under superfluous technical assumptions, this unconventional expectation formula provides an invaluable opportunity for students to appreciate the geometric meaning of expectations, which is overlooked in most undergraduate and graduate curricula, and serves as an efficient tool for the calculation of expected values that could be much more laborious by traditional means. For students’ benefit, this formula deserves a thorough in-class treatment in conjunction with the teaching of expectations. Besides clarifying some commonly held misconceptions and showing the pedagogical value of the expectation formula, this note offers guidance for instructors on teaching the formula taking the background of the target student group into account.     

论外部性影响也是创造价值的源泉

自马克思的《资本论》问世以来,劳动价值理论一直是学术界争论的焦点。通过对价值概念的重新厘清,指出商品中凝结的一般人类劳动与价值是两个相互独立的概念,并从理论与实践两方面指出了传统劳动价值理论的内在缺陷,认为劳动不是创造价值的唯一要素,外部性影响也是创造价值的源泉。为了解决价值的来源问题,本文认为劳动、劳动结合物、外部性影响三要素共同创造价值,并从理论以及实践两方面阐明了外部性影响也是创造价值的源泉。