TCHEBICHEV'S INEQUALITY IN THE CASE OF RANDOM VARIABLE OF SPECIAL DISTRIBUTION

Abstract

In this paper it is proved by elemental methods that the following inequalities exist. If the expected value of the probability variable is 0, the variance is a2 and its den- sity function satisfies the conditions then in the case of any positive e, inequality is valid. If the expected value of the discrete probability variable; is 0, the square of its scattering is a2 , then the following inequality applies a2 -9 -.,- ~ P(I;I ~ Ixil)· (i = 1,2, ... , n) 4x1 - 1 when conditions ensuring the concavity of distribution function and regarding its possible values and probability distribution are satisfied.