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ExpectedValue

As of Version 8.0, has been superseded by Expectation and NExpectation.

gives the expected value of the pure function f with respect to the values in list.

gives the expected value of the function f of x with respect to the values of list.

gives the expected value of the pure function f with respect to the symbolic distribution dist.

gives the expected value of the function f of x with respect to the symbolic distribution dist.
MORE INFORMATION
  • For the list , the expected value of f is given by .
  • For a continuous distribution dist, the expected value of f 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 expected value of f is given by where is the probability mass function of dist and summation is over the domain of dist.
  • The following option can be given:
Assumptions$Assumptionsassumptions to make about parameters
EXAMPLESCLOSE ALL
Basic Examples   (3)
Find the expected value of in a Poisson distribution:
Use a pure function:
Expected value for a list:
Find the expected value of in a Poisson distribution:
In[1]:=
Click for copyable input
Out[1]=
 
Use a pure function:
In[1]:=
Click for copyable input
Out[1]=
 
Expected value for a list:
In[1]:=
Click for copyable input
Out[1]=
Scope   (3)
Compute the expected value of any function:
Do the computation numerically:
Obtain expectations with conditions:
Options   (1)
Obtain results correct for given assumptions on symbols:
Applications   (2)
Obtain the raw moments of a distribution:
Construct a mixture density, here a Poisson-inverse Gaussian mixture:
Properties & Relations   (7)
of a function is the integral or sum of that function times the PDF:
of for real t is the CharacteristicFunction:
of a constant is the constant:
of a random variable is the Mean:
of the squared difference from the Mean is the Variance:
for a list is a Mean:
CentralMoment is equivalent to an expected value:
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