SOME RESULTS OF MOMENTS OF UNCERTAIN RANDOM VARIABLES

Chance theory is a mathematical methodology for dealing with indeterminate phenomena including uncertainty and randomness. Consequently, uncertain random variable is developed to describe the phenomena which involve uncertainty and randomness. Thus, uncertain random variable is a fundamental concept in chance theory. This paper provides some practical quantities to describe uncertain random variable. The typical one is the expected value, which is the uncertain version of the center of gravity of a physical body. Mathematically, expectations are integrals with respect to chance distributions or chance measures. In fact, expected values measure the center of gravity of a distribution; they are measures of location. In order to describe a distribution in brief terms there exist additional measures, such as the variance which measures the dispersion or spread, and moments. For calculating the moments of uncertain random variable, some formulas are provided through chance distribution and inverse chance distribution. The main results are explained by using several examples.