微分法在求多维连续型随机变量函数的概率密度中的应用

Application of Differential Method in Solving Probability Density of Functions of Multidimensional Continuous Type Random Variables

多维连续型随机变量的分布函数F(x1 ,… ,xn)与密度函数f(x1 ,… ,xn)的关系是 n x1 … xnF(x1 ,… ,xn) =f(x1 ,… ,xn) ,dF(x1 ,… ,xn) =f(x1 ,… ,xn)dx1 …dxn.利用这一关系给出了用微分法求多维连续型随机变量函数的概率密度的方法及实例 ,在许多情形下 。

The relation between distribution function F(x 1,...,x n) and density function f(x 1,...,x n) of multidimensional continuous type random variables is  nx 1...x n F(x 1,...,x n)=f(x 1,...,x n) .Based on this relation,the method and examples of solving probability density of functions of multidimensional continuous type random variables are given by use of differential method. In many cases,it is simpler than the ordinary methods.