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This subscript notation is obnoxious; one integrates over the whole probability space. |
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Line 104:
: <math>
P(E) = \int_\Omega P(E\mid x) P(x) \,dx = \int_\Omega \delta\big(E - E(x)\big) P(x) \,dx =
</math>
and, thus, estimating <math>P(E)</math> can be accomplished by estimating the expected value of the [[indicator function]] <math>A_E(x) \equiv \mathbf{1}_E(x)</math>, which is 1 when <math>E(x) \in [E, E + \Delta E]</math> and zero otherwise.
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