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BUILT-IN MATHEMATICA SYMBOL
NExpectation
NExpectation[expr, x
dist]
gives the numerical expectation of expr under the assumption that x follows the probability distribution dist.
NExpectation[expr, {x1, x2, ...}dist]
gives the numerical expectation of expr under the assumption that 
follows the multivariate distribution dist.
NExpectation[expr, {x1dist1, x2dist2, ...}]
gives the numerical expectation of expr under the assumption that 
, 
, ... are independent and follow the distributions 
, 
, ....
NExpectation[expr
pred, ...]
gives the numerical conditional expectation of expr given pred.
Details and Options
can be entered as x EscdistEsc dist or 
. 
can be entered as expr EsccondEsc pred or 
. - NExpectation works like Expectation except numerical summation and integration methods are used.
- For a continuous distribution dist, the expectation of expr is given by
where 
is the probability density function of dist and the integral is taken over the domain of dist. - For a discrete distribution dist, the probability of expr is given by
where 
is the probability density function of dist and the summation is taken over the domain of dist. - NExpectation[expr, {x1dist1, x2dist2}] corresponds to NExpectation[NExpectation[expr, x2dist2], x1dist1] so that the last variable is summed or integrated first.
- N[Expectation[...]] calls NExpectation for expectations that cannot be done symbolically.
- The following options can be given:
-
AccuracyGoal ∞ digits of absolute accuracy sought PrecisionGoal Automatic digits of precision sought WorkingPrecision MachinePrecision the precision used in internal computations Method Automatic what method to use
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