Expectation

Expectation[expr,xdist]
gives the expectation of expr under the assumption that x follows the probability distribution dist.

Expectation[expr,xdata]
gives the expectation of expr under the assumption that x follows the probability distribution given by data.

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

Expectation[expr,{x1dist1,x2dist2,}]
gives the expectation of expr under the assumption that , , are independent and follow the distributions , , .

Expectation[exprpred,]
gives the conditional expectation of expr given pred.

Details and OptionsDetails and Options

  • Expectation is also known as expected value.
  • can be entered as x EscdistEsc dist or .
  • can be entered as expr EsccondEsc pred or .
  • 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.
  • For a dataset data, the expectation of expr is given by Sum[expr,{x,data}]/Length[data].
  • Univariate data is given as a list of values and multivariate data is given as a list of vectors .
  • Expectation[expr,{x1dist1,x2dist2}] corresponds to Expectation[Expectation[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:
  • Assumptions$Assumptionsassumptions to make about parameters
    GenerateConditionsFalsewhether to generate conditions on parameters
    MethodAutomaticwhat method to use

Background
Background

Introduced in 2010
(8.0)