You have studied the number of people waiting in line at your bank on Friday afternoon at 3 pm for many years, and have created a probability distribution for 0, 1, 2, 3, or 4 people in line. The probabilities are 0.1, 0.3, 0.4, 0.1, and 0.1, respectively. What is the expected number of people (mean) waiting in line at 3 pm on Friday afternoon?
The expected number in this case can be thought of as a weighted average. It is best arrived at by summing the probability of a given number by that number. So, in this case:
The mean (or expected value or mathematical expectation or, simply, average) is equal to
In general, if a random variable
The above is a definition for discrete random variable taking a finite number of values. More complex cases with infinite number of values (countable or uncountable) require involvement of more complex mathematical concepts.
A lot of useful information on this subject can be found on the Web site Unizor by following the menu item Probability.