一类古典概型的公式解

针对一类古典概型,通过将基本事件数转化为不定方程的解的个数,并利用组合方法将其求出,进而可以得到该古典概型的公式解.     

古典概型知识结构解析

古典概型是最基本的一种概率模型,在实际中有广泛的应用.该模型比较简单,学习起点可以基于高中数学的一些相关知识,因而成为向高中生介绍概率知识的载体之一.     

一类古典概率问题的解法探究

研究了一类需要预测长期趋势的古典概型问题,其将来的状态只与现在的状态有关,与以前的状态无关.分别应用全概率公式和Markov链,给出该类问题的两种不同解法.     

概率母函数在求非负整值随机变量分布的应用

主要讨论概率母函数法求解古典概率问题的应用,以及某些非负整值的随机变量的分布.     

求古典概率时易发生的一类错误

古典概型是概率论的一个重要部分,它有助于我们直观地理解概率论的许多基本概念,掌握抽样调查等统计方法．它的计算方法大致可分为：①直接计算②利用概率的基本性质,基本公式及事件间关系进行计算．其中,直接计算是基础,组合分析方法是重要工具．学生在用组合数方法求古典概率时常会得出错误的结论而不知错在何处．剖析错误原因,对正确掌握解题方法很有必要．下面举例说明在用组合数方法求古典概率时可能会出现的一类问题．例1从5副不同的手套中任取4只手套,求其中至少有两只手套配成一副的概率．错误解法：记事件A=｛任取4只手套…     

恰当选取样本空间，简化古典概率计算

用概率的古典定义计算概率时 ,首先要确定随机试验是什么 ,从而确定出样本空间 .若样本空间中的各基本事件在试验中的出现是等可能的 ,则可由古典概率公式求各随机事件的概率 .但同一问题随试验的内容不同可选取不同的样本空间 ,只要满足样本空间中的基本事件只有有限个 ,且它们的出现是等可能的 ,就可用古典概率公式计算 ,且计算出的结果必定相同 .因此试验的样本空间选得好 ,问题解决起来就会简便一点 .下面举例说明 .在下面的例子中均以 N表示基本事件总数 ,M表示所求事件包含的基本事件数 .例 1　袋内有 a个白球与 b个黑球 ,每次从袋中…     

不尽相异问题的古典概型概率的计算

不尽相异问题的古典概型概率的计算是概率论教学中学生不易理解的问题之一，本文通过例题从思维方法及具体步骤等方面说明这一解题思想。     

巧选样本空间 简解古典概型

同一个古典概型问题由于考虑的角度不同,其解法繁简差别较大.因此,在选取样本空间时,务必抓住欲求事件的本质,而把其它无关的因素抛开,以简化求解过程. 例1袋中装有a只白球,b只黑球,每次从中任取一个,取后不放回,求第k次(0相似文献   

数学期望在古典概率计算中的应用

讨论一些涉及多次取球的古典概率的计算问题,利用一个期望和概率之间关系的结论将概率问题转化为期望问题,然后根据期望的递推公式得出答案.     

古典概率问题解法探讨

古典概率问题解法探讨翁泽群（汕头供销学校５１５０４１）普遍认为古典概率的习题难做，不易掌握规律．问题在于古典概率是处理随机现象的，其思维方法与其他数学学科相比有独特之处，解决问题时更着重概念与思路，学生一下子不易领会．因此，在进行古典概率的教学时，注...     

A solution to the distribution problems arising in the studies of a two-sex population process

Given a population of two sexes, the birth rate of one sex of which depends upon the population size of the other, it is very difficult to find an explicit expression for the probability distribution of the former. In this paper we have explicitly found the probability generating function of the joint distribution from which individual probability distributions and, in particular, moments of all orders in each case can be obtained in principle. As an example, using this probability generating function we have worked out explicitly the first and second order moments of the male and female populations and the explicit expression for the distribution of the male population in a particular case. This method can be successfully applied for the same purpose in the studies of chemical and biological processes where the synthesis or production of one species depends upon the concentration of another species.     

一类含非线性项的位势方程

讨论了一类含非线性项的位势方程 ,得到了这个问题古典解存在唯一性 .     

一类新的解析函数族

定义了一族解析函数B(λ,α,β),导出该族中函数的积分表达式;借助算子理论建立B(λ,α,β)的包含关系,讨论端点性质;由此推出族中函数的偏差定理.     

Life-span of Classical Solutions to Nonlinear Wave Equations in Two-space-dimensions II

In two-space-dimensional case we get the sharp lower bound of the life-span of classical solutions to the Cauchy problem with small initial data for fully nonlinear wave equations of the form ◻u = F (u, Du, D_zDu) in which F(\hat{λ}) = O(|\hat{λ}|^{1+α}) with α = 2 in a neighbourhood of \hat{λ} = 0. The cases α = 1 and α ≥ 3 have been considered respectively in [1] and [2].     

一类双曲型方程的Hamilton算子半群方法

将一类双曲型方程混合问题转换成一阶抽象Cauchy问题,证明所得Hamilton算子矩阵H在相应空间中生成压缩半群,并借助Fourier变换,采用一致连续半群做逼近的方法,得到H所生成的压缩半群,进而给出了问题的古典解.     

A Class of Strong Limit Theorems and Moment Generating Function Method

In virtue of the notion of likelihood ratio and moment generating function,the limit properties of the sequences of absolutely continuous random variables are studied,and a class of strong limit theorems represented by inequalities with random bounds are obtained.     

System-Wide Probabilities for Systems with Runs and Scans Rules

Systems that include multiple decision rules are encountered in many fields. We focus on systems with several states or levels where the rules determining when and how to move between the levels are based on runs or scans. Our target is to evaluate the proportion of time spent at each level. This information is valuable since it is required for constructing various cost functions. In this paper we address two questions: How to incorporate the system of levels and decision rules into a probabilistic setting and which measures to use in order to evaluate the proportion of time spent at each level. We take a waiting-time approach, and use special features of runs and scans distributions in order to investigate long and short-term measures of the time spent at the different levels of a system. We introduce a short term per-cycle measure and compare it with the finite-time measure. We find that the two measures can differ significantly.