一维与二维连续随机变量的函数的分布  

Distribution of continuous random variable of one and two dimentions

作　　者：张洪川[1] 盛克敏[1] 马丽琼[1] 

机构地区：[1]西南交通大学峨眉校区基础课部,四川峨眉614202

出　　处：《西南民族大学学报（自然科学版）》2005年第6期995-997,共3页Journal of Southwest Minzu University(Natural Science Edition)

摘　　要：现行“概率论与数理统计”教材中关于一维与二维随机变量函数的概率分布讲法上不够简练,在系统性上有欠完备,试图给出一定改进及讲法更新方面的一些建议。其中心内容是对一维随机变量单调函数的概率密度函数避免用积分表示,直接用复合函数求导方法推出;对非单调函数用划分单调区间办法给出函数概率密度的一般表达式;对二维变量试图用二维换元法给出推算二维函数分布的统一方法。In present teaching materials of “Theory of possibility and mathematical statistics”, the statement of probability distribution of 1-D and 2-D random variables is not succinct and systematic. We derive probability density function of random variables without using an integral representation. As first step, for 1-D monotone function of random variable, the method of taking derivatives of composite functions is used. Then, for non-monotone function, we divide the interval of variables into several so-called monotone regions. In this case probability density is given. To 2-D case, the method is the same, and the only difference is that the variable transformation is a little bit complicated.

关 键 词：一维随机变量 二维随机变量 函数分布 函数变换 

分 类 号：G642[文化科学—高等教育学]