数学期望几个公式的证明

Proofs of Several Formulas on Mathematical Expectation

《概率统计》教学中,在讲授数学期望这一节时,许多学生认为连续型随机变量或连续型随机向量的几个计算公式给出比较突然,不易理解.因此在已知离散型随机变量数学期望的计算公式的前提下,利用微积分的极限思想,说明了这几个公式是如何成立的。不仅有助于学生理解掌握这几个公式,而且使学生领略极限在解决问题时的妙用。

In the processing of teaching mathematical expectation, many students think that the calculation formulas of continuous random variables and continuous random vector are given suddenly ,so it is not easy to understand. Therefore, under the condition that we known calculation formulas of mathematical expectation about discrete random variables, we have proved these formulas about the continuous random variables and the continuous random vector in this article by means of the limit.