<P> In probability theory, the expected value of a random variable, intuitively, is the long - run average value of repetitions of the experiment it represents . For example, the expected value in rolling a six - sided dice is 3.5, because the average of all the numbers that come up in an extremely large number of rolls is close to 3.5 . Less roughly, the law of large numbers states that the arithmetic mean of the values almost surely converges to the expected value as the number of repetitions approaches infinity . The expected value is also known as the expectation, mathematical expectation, EV, average, mean value, mean, or first moment . </P> <P> More practically, the expected value of a discrete random variable is the probability - weighted average of all possible values . In other words, each possible value the random variable can assume is multiplied by its probability of occurring, and the resulting products are summed to produce the expected value . The same principle applies to an absolutely continuous random variable, except that an integral of the variable with respect to its probability density replaces the sum . The formal definition subsumes both of these and also works for distributions which are neither discrete nor absolutely continuous; the expected value of a random variable is the integral of the random variable with respect to its probability measure . </P>

What is mathematical expectation of a random variable