# 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 {x1,x2,} follows the multivariate distribution dist.

Expectation[expr,{x1dist1,x2dist2,}]

gives the expectation of expr under the assumption that x1, x2, are independent and follow the distributions dist1, dist2, .

Expectation[exprpred,]

gives the conditional expectation of expr given pred.

# Details and Options • Expectation is also known as expected value.
• xdist can be entered as x dist dist or x[Distributed]dist.
• exprpred can be entered as expr cond pred or expr[Conditioned]pred.
• 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 {v1,v2,} and multivariate data is given as a list of vectors {{v11,,v1m},{v21,,v2m},}.
• 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 \$Assumptions assumptions to make about parameters GenerateConditions False whether to generate conditions on parameters Method Automatic what method to use TargetUnits Automatic units to display in the output

# Examples

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## Basic Examples(3)

Compute the expectation of a polynomial expression:

 In:= Out= In:= Out= In:= Out= In:= Out= Compute the expectation of an arbitrary expression:

 In:= Out= In:= Out= In:= Out= Compute a conditional expectation:

 In:= Out= In:= Out= ## Possible Issues(1)

Introduced in 2010
(8.0)
|
Updated in 2016
(10.4)