Statistics for Throwing a Die Three Times

Consider the experiment of repeatedly throwing a die three times. Let , and 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.

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