This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# 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As of Version 8.0, has been superseded by Expectation and NExpectation.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.
• 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 \$Assumptions assumptions to make about parameters
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:
 Out[1]=

Use a pure function:
 Out[1]=

Expected value for a list:
 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:
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: