The expected value of a random variable, which is the weighted average of its all possible values with their respective probabilities as the corresponding weights, had already been defined with the help of arithmetic mean and the definition was termed as mathematical expectation. The same has, in this study, been defined made with the help of geometric mean and harmonic mean. In order to be free from confusion, the existing definition of mathematical expectation will be termed as arithmetic expectation since it is based on arithmetic mean. The two definitions of mathematical expectation to be defined with the help of geometric mean and harmonic mean will be termed as geometric expectation and harmonic expectation respectively. This article describes these two definitions with numerical examples.