An Inequality for Some Functions of Continuous Random Variables

Abstract

We establish new inequalities for moment generating function of a continuous random variable; characteristic function of a continuous random variable, power spectral density (or power spectrum) of a continuous-time WSS random process and autocorrelation function of a continuous-time WSS random process, using a form of the Cauchy-Bunyakovsky-Schwarz inequality. Our new inequalities obey the general form                        ()    

Keywords and phrases. Cauchy-Bunyakovsky-Schwarz inequality, moment generating function, characteristic function, continuous-time WSS random process, power spectral density.

2010 Mathematics Subject Classification. 26D07, 60E15