Document Type: Research Paper


1 Department of Statistics, University of Sistan and Baluchestan, Zahedan, Iran

2 College of Mathematical and System Sciences, Xinjiang University, Urumqi 830046, China


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.


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