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Statistics[ExpectedValue] - compute expected values

Calling Sequence

ExpectedValue(A, f, ds_options)

ExpectedValue(M, f, ds_options)

ExpectedValue(X, f, rv_options)

ExpectedValue(X, rv_options)

Parameters

A

-

data sample

M

-

Matrix data set

X

-

algebraic; distribution, random variable

f

-

operator; any function

ds_options

-

(optional) equation(s) of the form option=value where option is one of ignore, or weights; specify options for computing the expected value of a data set

rv_options

-

(optional) equation of the form numeric=value; specifies options for computing the expected value of a random variable

Description

• 

For a data set A (given as e.g. a Vector) or a Matrix data set M, the ExpectedValue function computes the expected value of f with respect to the sample distribution of A or of the columns of M, respectively.

• 

For a random variable X the ExpectedValue command computes the expected value of f(X). If X is an expression involving random variables, then the expected value of X is computed.

• 

The first parameter X is a random variable or an algebraic expression involving random variables.

• 

The second parameter is a function.

Computation

• 

By default, all computations involving random variables are performed symbolically (see option numeric below).

• 

All computations involving data are performed in floating-point; therefore, all data provided must have type[realcons] and all returned solutions are floating-point, even if the problem is specified with exact values.

• 

For more information about computation in the Statistics package, see the Statistics[Computation] help page.

Data Set Options

  

The ds_options argument can contain one or more of the options shown below. More information for some options is available in the Statistics[DescriptiveStatistics] help page.

• 

ignore=truefalse -- This option controls how missing data is handled by the ExpectedValue command. Missing items are represented by undefined or Float(undefined). So, if ignore=false and A contains missing data, the ExpectedValue command will return undefined. If ignore=true all missing items in A will be ignored. The default value is false.

• 

weights=Vector -- Data weights. The number of elements in the weights array must be equal to the number of elements in the original data sample. By default all elements in A are assigned weight 1.

Random Variable Options

  

The rv_options argument can contain one or more of the options shown below. More information for some options is available in the Statistics[RandomVariables] help page.

• 

numeric=truefalse -- By default, the expected value is computed using exact arithmetic. To compute the expected value numerically, specify the numeric or numeric = true option.

Examples

withStatistics:

X:=RandomVariableNormala,b:

Y:=RandomVariableNormalc,d:

ExpectedValueX2

a2+b2

(1)

ExpectedValueX+Y

a+c

(2)

ExpectedValueXa2

b2

(3)

Z:=RandomVariableExponential2:

A:=SampleZ,105:

ExpectedValueZ2

8

(4)

ExpectedValueA,t→t2

8.00071728582744

(5)

Consider the following Matrix data set.

M:=Matrix3,1130,114694,4,1527,127368,3,907,88464,2,878,96484,4,995,128007

M:=31130114694415271273683907884642878964844995128007

(6)

We compute the expected value of the natural logarithm of each of the column data sets.

ExpectedValueM,ln

1.132592096027196.9703129995667711.6064364945012

(7)

See Also

Statistics, Statistics[CentralMoment], Statistics[Computation], Statistics[Distributions], Statistics[RandomVariable]

References

  

Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998.  Vol. 1: Distribution Theory.


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