On lower bounds for the variance of functions of random variables with weighted distributions

چکیده مقاله

In this paper, based on the obtained characterization via the lower bounds for the variance of a function of random variable X, we nd a characterization of the weighted function corresponding to density function f(x), in terms of Cherno-type inequalities. Subsequently, by using the new characterization, we derive the lower bounds for the variance of a function of the weighted random variable. Moreover, assuming that X is DFR [decreasing failure rate] we nd an lower bound for the variance of this function with specific weight functions.