We derive some inequalities involving first four central moments of discrete and continuous distributions. Bounds for the eigenvalues and spread of a matrix are obtained when all its eigenvalues are real. Likewise, we discuss bounds for the roots and span of a polynomial equation.

中文翻译：

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中心矩和矩阵传播的不等式

我们推导出一些涉及离散和连续分布的前四个中心矩的不等式。当矩阵的所有特征值都是实数时，就可以获得矩阵的特征值和扩展的界限。同样，我们讨论多项式方程的根和跨度的界限。