If X and Y are discrete random variables in finite case, then using the inequality of Cauchy-Schwarz, we will obtain another inequality expressed by the variance and covariance. The aim of this paper is to obtain a new refinement of discrete version of Gr¨uss inequality. In the final we show that we can structure the set of random variables with equal probabilities as a Hilbert space and as a seminormed vector space.
Digital Object Identifier (DOI)
Minculete, Nicuşor; Rațiu, Augusta; and Pečarić, Josip
"A Refinement of Grüss Inequality via Cauchy-Schwarz’s Inequality for Discrete Random Variables,"
Applied Mathematics & Information Sciences: Vol. 09:
1, Article 13.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss1/13