Difference between revisions of "Bernoulli experiment"
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== Expectation and Variance == | == Expectation and Variance == | ||
| − | If the | + | If the occurrence of a success is encoded as '''1''' and the occurrence 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> | <math>\mathbf{E}[X] = p \cdot 1 + q \cdot 0 = p</math> | ||
Revision as of 15:58, August 25, 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 occurrence of a success is encoded as 1 and the occurrence 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>.