Consider the experiment of repeatedly throwing a die three times. Let
be the outcomes of the first, second and third throws, respectively. Consider the statistic
. This Demonstration samples the distribution of
as a result of repeating the experiment a number of times. As a consequence of the properties of the expected value and variance, the theoretical mean, variance and standard deviation are
. This Demonstration shows that the observed values of
after a large number of repeats give average and standard deviation very close to the theoretical values.