In this research article we obtained some inequalities between moments of 1st and 2nd order for a continuous distribution over the interval [x, y], when infimum and supremum of the continuous probability distribution is taken into consideration. These inequalities have shown improvement and are better than those exist in literature. Inequalities also obtained for continuous random variables which vary in [x, y] interval, such that the probability density function (pdf) (t) become zero in [p,

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...  [x, y].The improvement in inequalities have been shown graphically. Here in this paper we deduced some existing inequalities by using the inequalities obtained in Theorem 2.1 and Theorem 2.2.