# ExpectedValue

As of Version 8.0, ExpectedValue has been superseded by Expectation and NExpectation.

ExpectedValue[f,list]

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

ExpectedValue[f,list,x]

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

ExpectedValue[f,dist]

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

ExpectedValue[f,dist,x]

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

# Details and Options

• 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

# Examples

open allclose all

## Basic Examples(3)

Find the expected value of in a Poisson distribution:

 In[1]:=
 Out[1]=

Use a pure function:

 In[1]:=
 Out[1]=

Expected value for a list:

 In[1]:=
 Out[1]=