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Consider a sequence of independent tosses of a fair coin. The possible outcomes could be heads or tails. Let us denote the possible outcome of the i-th trial by $X\_i$, where we encode head as 1 and tail as 0. Now let denote the mean value after trials, namely

:$M\_N\; =\; \backslash frac\{1N\}\backslash sum\_\{i=1\}^\{N\}\; X\_i$.}}

Then lies between 0 and 1. From the law of large numbers it follows that as N grows, the distribution of converges to (the expected value of a single coin toss).

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