Expectation (math)
From Conservapedia
The mathematical expectation of a continuously distributed random variable X with probability density function f(x) is
![\mbox{E}[X]
=\int\limits_{-\infty}^\infty
x
f(x)dx.](images/math/c/9/a/c9abdceca463cfe513232302351988f6.png)
The expectation is also known as the mean of X.
The expectation with respect to some function g(X) where X is distributed according to f(x) is
![\mbox{E}[g(X)]
=\int\limits_{-\infty}^\infty
g(x)
f(x)dx.](images/math/3/6/d/36dd17389c896d77289774a58ac595b6.png)
For a discretely distributed random variable X with probability mass function pk it is
E[X] = ∑ pkxk. k
