关于非负随机变量的几个矩不等式

Some Moment Inequalities of Nonnegative Random Variablew

设X是非负随机变量且0<m≤X≤M,本文讨论两个Cauchy型矩不等式的反向,得到以下不等式:E(X2)-(E(X))2≤41(M-m)2,E(X2)-E(X)≤4((M M-+mm))2,E(X)-(E(X-1))-1≤(M-m)2,E(X)E(X-1)≤(M4+Mmm)2,并利用所得结果给出一些反向Cauchy-Schwarz不等式.

Let X be an nonnegative random variable and 0〈m≤X≤M, converse of two Cauchy-type inequalities are discussed, some moment inequalities of X are obtained as follow： E（X^2）-（E（X））^2≤1/4（M-m）^2, √E（X^2） -E（X）≤（M-m）^2/4（M＋n）, E（X）-E（X^-1））^-1≤（√M -√m）^2, E（X）E（X^-1）≤（M＋m）^2/4Mm, and several converse Cauchy-Schwarz inequalities are also derived.