NExpectation

NExpectation[expr, xDistributeddist]
gives the numerical expectation of expr under the assumption that x follows the probability distribution dist.

NExpectation[expr, {x1, x2, ...}Distributeddist]
gives the numerical expectation of expr under the assumption that follows the multivariate distribution dist.

NExpectation[expr, {x1Distributeddist1, x2Distributeddist2, ...}]
gives the numerical expectation of expr under the assumption that , , ... are independent and follow the distributions , , ....

NExpectation[exprConditionedpred, ...]
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, {x1Distributeddist1, x2Distributeddist2}] corresponds to NExpectation[NExpectation[expr, x2Distributeddist2], x1Distributeddist1] 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:
  • AccuracyGoaldigits of absolute accuracy sought
    PrecisionGoalAutomaticdigits of precision sought
    WorkingPrecisionMachinePrecisionthe precision used in internal computations
    MethodAutomaticwhat 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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