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| An '''expected value''' is the estimated outcome of an event. The math notation is ''E[A]''. | An '''expected value''' is the estimated outcome of an event. The math notation is ''E[X]''. |
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| For a discrete distribution, the expected value is generally ''Σ x P(x)''. | For a discrete distribution, the expected value of ''X'' is generally ''Σ x P(x)'' (for all ''X=x''). |
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| For a continuous distribution, the expected value is generally ''∫ x P(x) dx''. | For a continuous distribution, the expected value of ''X'' is generally ''∫ x P(x) dx'' (for all ''X=x''). |
Expected Values
An expected value is the estimated outcome of an event. The math notation is E[X].
Contents
Evaluation
For a discrete distribution, the expected value of X is generally Σ x P(x) (for all X=x).
For a continuous distribution, the expected value of X is generally ∫ x P(x) dx (for all X=x).
Bernoulli
For a Bernoulli-distributed variable (taking value 1 with probability p and value 0 with probability 1-p), the expected value is p.
E[X] = Σ x P(x)
E[X] = (0) P(0) + (1) P(1)
E[X] = P(1)
E[X] = p