An inequality for some functions of continuous random variables

الملخص EN

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 f αx ≤ f{α + βx}f{α − βx}