Inequalities for variances of some functions of random variables
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In this note we prove some inequalities for variances and other measures of deviation of functions of random variables. Based on these inequalities we find some corollaries concerning the variances of fractional powers of random variables and of sums of independent random variables.
KeywordsIndependent Random Variable Fractional Calculus Fractional Power Positive Random Variable Chebyshev Inequality
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- Wolfe, S. J.: On moments of probability distribution functions. in: Lect. Notes in Math., Vol. 457 (Fractional calculus and applications, ed. by B. Ross) 306–316 Springer-Verlag, Berlin-Heidelberg (1975)Google Scholar