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The standard example is ''tossing a coin''.
The standard example is ''tossing a coin''.
== Expectation and Variance ==
If the occurence of a success is encoded as '''1''' and the occurence of a failure with '''0''', then a probability of a success of ''p'' (and therefore, of a failure as ''q=1-p'') leads to an expectation of
<math>\mathbf{E}[X] = p \cdot 1 + q \cdot 0 = p</math>
The variance is <math>Var(X) = \mathbf{E}[(X - \mathbf{E}[X])^2] = p(1-p)^2 + q(0-p)^2 = pq </math>.
[[category:Probability and Statistics]]
[[category:Probability and Statistics]]