2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65390In the paper I study properties of random polynomials with respect to a general system of functions. Some lower bounds for the mathematical expectation of the uniform and recently introduced integral-uniform norms of random polynomials are established. {\sc Key words and phrases:} Random polynomial, estimates for maximum of random process, integral-uniform norm.To be puslished in Mathematical NotesProbabilityClassical Analysis and ODEs60G99; 60G70; 26D15text