众所周知,随机变量X的方差DX是X的一个重要的特征数字,它刻画了随机变量X离开其“中心”位置—EX的偏差程度.由于DX=EX2-(EX)2≥0,再加上DX=0的充要条件为X服从单点分布,正是这一“极端”情形,为我们用概率方法解决中学数学有关问题提供了契机.本文将利用这一简单结论,构造适当 It is well known that the variance DX of a random variable X is an important characteristic of X. It characterizes the degree of deviation of the random variable X from its “center” position -EX. Since DX = EX2 - (EX) 2 ≧ 0, The necessary and sufficient condition for DX = 0 is that X follows a single point distribution, and it is this “extreme” situation that provides an opportunity for us to solve the problem of high school mathematics by using the probabilistic method.This paper will make use of this simple conclusion to construct an appropriate