Expected Value

Mathematical expectation is the expected value of random phenomenon, also sometimes called an expected value. After the probability distribution of a random variable has been constructed, the next task is to calculate the mean of that random variable. In other words, one can say that the mathematical expectation of the random variable is computed. In the case of a discreet random variable, the mathematical expectation will be given by the mathematical formula as, E(X)=and in the case of continuous random variable, the mathematical expectation will be given by the mathematical formula as, E(X)=. In the discreet case of mathematical expectation formula, p(x) denotes the probability mass function and f(x), in the continuous case of mathematical expectation formula, denotes the probability density function.
The mathematical expectation of an indicator variable can be zero if there is no occurrence of an event A, and the mathematical expectation of an indicator variable can be one if there is an occurrence of an event A. Thus, it is a useful tool to find the probability of event A.