基于二重积分换元法的概率问题研究

Study on Probability Problems Based on Double Integral Substitution Method

高等数学与概率统计是大学本科非数学专业的2门重要基础课,高等数学是基础课程,而概率统计更加注重应用。该项研究通过对一些实例的解答,重点阐述二重积分换元法在概率问题研究中所起的作用,如利用二重积分换元法求二维随机变量的联合概率密度及某一事件的概率;求二维正态随机变量X、Y的高阶混合中心矩等,一方面揭示概率统计与高等数学的联系密切,另一方面拓宽解题思路,为进一步研究相关概率问题打下坚实基础。

Higher mathematics and probability statistics are two important basic courses of undergraduates majoring in non-mathematics.Of these two courses,higher mathematics is the basis,whereas probability statistics pays more attention to application.Some examples were given to illustrate the role of double integral commutation method in probability problem study,such as using the double integral commutative method to find the joint probability density of two-dimensional random variables and the probability of an event or finding the high-order mixed central moments of two-dimensional normal random variables X and Y,etc.On the one hand,it reveals that probability statistics is closely related to higher mathematics,and on the other hand,it widens our thoughts in solving problems,laying a solid foundation for further research on related probability problems.