卷积公式的推广及应用

Extension and Application for the Convolution Formula

将概率论中用于求两个连续型随机变量和的概率密度函数的卷积公式进行了推广,推广后的公式可以用于求形如Z=aX+bY(ab≠0)的二维连续型随机变量函数的概率密度函数.对推广后的公式首先给出了证明,然后将推广后的公式应用于求解具体的算例,从而验证了公式的有效性.

The article has given the extension about the convolution formula. The new formula may give two- dimensional random variable function＇s probability density function for Z=aX＋by（ab≠0）. Firstly, this paper gives the formula＇s identification. Then, an example is illustrated to show that the formula proposed in this paper is feasible and effective.