一常见不等式的推广及其概率意义

A Generalization and Probability Meaning of a Common Inequality

本文应用Jensen不等式证明了著名不等式：调和平均值≤几何平均值≤算术平均值．并将该不等式推广至非常一般的形式．文中给出该不等式所表示的概率意义，并用以解释日常生活中的一常见现象．

A new prove method and a generalization of the famous inequality 'harmonic mean-gemetric mean-arithmetic mean inequality' is given by means of Jensen Inequality in this paper.The probability meaning of geometric mean-arithmetic mean inequality is studied and used to explain a common phenomeron in agriculture.