A fair six-sided die exhibits a uniform distribution of outcomes. That is, we expect that there is an equally likely chance of each side coming up. For the roll of a single die, the distribution has a mean of 3.5 and a standard deviation of . This doesn’t say that you will get 3.5 on a roll, just that, over time, that will be the arithmetic average. This is an application of the Law of Large Numbers, which says that, as we repeat an experiment, the sample mean should converge toward the true mean.
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