概率论中定积分计算的若干常见错误与剖析

Some Common Faults and Analysis of Definite Integral Calculation in Probability Theory

定积分在概率论计算中发挥着极其重要的作用,但是学生在涉及相关定积分的计算中经常出现错误。为了消除这些错误,结合具体计算实例,分别列举分布函数、概率密度函数、数学期望求解过程中经常出现的错误,对产生错误的原因进行具体剖析,找出产生错误的根源并给出详细的解答,同时指出了教学注意事项,为教师在概率论教学中更加有效地处理涉及定积分的问题提供参考。

Definite integral plays very important role in calculation of probability theory,but students often make mistakes in the calculation related to definite integral.In order to eliminate these faults,combined with specific calculation examples,some common faults in the solving process of distribution function,probability density function,mathematical expectation are listed.The reasons for these faults are analyzed,the root of the faults are found,the detailed correct answers are given,and some teaching attention matters are proposed which provides some references for teachers to deal with the problems involving definite integral more effectively in probability theory teaching.