Although everyone has the concept of average, a fundamental difference is that expectation is the average of the population of random variables, and average is the average of samples taken from the population. The former is the theoretical value and ideal value, while the latter is the statistics observed in reality.

For example, the number of points x obtained by throwing a six-sided even dice is a random variable, and the expected value of x is 3.5(= [1+2+3+4+5+6]/6). What about the average? The average number of points obtained by throwing this dice many times-for example, five times-may be different from the expected 3.5 in each experiment.