AN INEQUALITY FOR SOME FUNCTIONS OF CONTINUOUS RANDOM VARIABLES

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^2(αx) ≤ f{(α+β)x}f{(α−β)x} (α,β∈ℝ)