侦辑问题及其恒等式

以侦辑工作中的实际问题为背景，建立了一个随机数学模型，针对要解决的两种问题，又将原模型化为寻求随机变量的分布列及其数字特征的问题和寻求Markov链极限分布的问题，对犯人如实招供的情况，求出了破案需要调查的次数的分布，并给出了破案平均时间和方差的算式，还由此得到一个新的数学恒等式，对犯人隐瞒自己罪行的情况，求出了Markov链的一步转移概率矩阵和极限分布，并用特征函数方法得到了同样的结果。

Problems of Detection and Its Identity

A stochastic model of detective problem was built and was transformed into the problems of finding the distributions and the numerical characters of inquiry number and the problems of finding the limit distributions of the Markov chain. As to the cases in which the criminal makes a confession of his crime,the probability distribution of inquiry number for cracking a criminal case was calculated and the formula to calculate the mean time and the variance of inquiry number was given,from which a new identity resulted. As to the cases in which the criminal denies his crime,the one-step transform probability matrix in Markov chain and the final distribution of inquiry number for cracking a criminal case were obtained. The same results were obtained by the methods of characteristic functions.