BUILT-IN MATHEMATICA SYMBOL

# NExpectation

NExpectation[expr, xdist]
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[exprpred, ...]
gives the numerical conditional expectation of expr given pred.

## Details and OptionsDetails 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

## ExamplesExamplesopen allclose all

### Basic Examples (3)Basic Examples (3)

Compute the expectation of a polynomial expression:

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Compute the expectation of an arbitrary expression:

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Compute a conditional expectation:

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