关于随机变量的概率密度及其求法摘要本文主要介绍了连续型随机变量函数从一维到多维的概率密度函数的解法，以及通过各自的常见例题，来使我们对每一种方法有进一步的理解和掌握。通过分布函数求导法，经典公式法，分段区间法，来求解，其中分布函数求导法用的比较普遍，因其所受的条件影响较少，也易于理解。二维随机变量的概率密度主要通过分布函数求导，卷积公式，变量变换，且在变量变换基础上进一步引入增补变量的方法，在卷积公式的基础上推导了连续型二维随机变量(X,)的线性函数Z=X+bY,(ab≠O)的概率密度公式，对于n维随机变量函数给出了一般方法和定点方法。关键词随机变量概率密度积分分布函数法On the probability density of random variable and its solutionAbstract This paper mainly introduces the methods to solve the probability density function ofone-dimensional to multi-dimensional continuous random variable function,and through theircommon examples,we have a further understanding and mastery of each method.Through thedistribution function derivation method,classical formula method,subsection interval method,to solve,the distribution function derivation method is more common,because it is less affectedby the conditions,and easy to understand.The probability density of two-dimensional randomvariables is mainly determined by distribution function derivation,convolution formula andvariable transformation,and the method of adding variables is further introduced on the basisof variable transformation,and the probability density calculation formula of linear function ofcontinuous two-dimensional random variables is derived on the basis of convolution formulaThe general method and the fixed point method are given.Key words Random variable Probability density Integral Distribution function method目录1.11.21.3连续型随机变量的分布的概率密度.···1.4分布函数的求导法…41.541.61.71.81.9二维连续性随机变量的函数的概率密度及其求法……··102.1102.1.1102.1.2随机变量的边缘分布概率密度·112.1.3112.1.42.22.3132.4142.5变量变换法。152.6利用变量变换…2.7172.82.9182.1020