二重积分换元法视角下的连续卷积公式  

Continuous Convolutional Formula from the Perspective of Double Integral Transformation Method

作　　者：胡永生[1] HU Yongsheng(Public Education Department,Fujian Vocational College of Agriculture,Fuzhou 350119,China)

机构地区：[1]福建农业职业技术学院公共教学部,福建福州350119

出　　处：《高等数学研究》2025年第2期4-9,共6页Studies in College Mathematics

摘　　要：主要研究如何从先修课程高等数学中借力,在二重积分换元法的视角下,认识概率论与数理统计课程中,有关二维随机变量函数的分布所涉及的卷积公式这一教学重点、难点;让学生深入了解卷积公式的来由,进而熟练掌握使用卷积公式来处理相关问题.This paper explores how to leverage advanced mathematics from prerequisite courses to address key challenges in teaching the convolution formula for two-dimensional random variables in probability theory and mathematical statistics.Using the double integral transformation method,it aims to help students understand the origin of the convolution formula and master its application to related problems.

关 键 词：二重积分 换元法 二维随机变量 雅可比行列式 卷积公式 

分 类 号：O211.5[理学—概率论与数理统计]