Difference between revisions of "Bernoulli experiment"
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The standard example is ''tossing a coin''. | The standard example is ''tossing a coin''. | ||
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| + | == 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 | ||
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| + | <math>\mathbf{E}[X] = p \cdot 1 + q \cdot 0 = p</math> | ||
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| + | 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]] | ||
Revision as of 12:56, August 16, 2010
A Bernoulli experiment (or Bernoulli trial) is the simplest non-trivial random experiment imaginable: it's an experiment of which the outcome is random and can be either of two possibilities: success and failure.
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>.