The mean or expectation of a continuous random variable X is given by

where f(x) is the probability density function of X. This represents the average value of X and is usually denoted by the symbol μ. To find the expected value of any function of X, say h(X), we extend the above definition in the following manner.

One very important example of this is h(X) = X², note however that E[X²] is not the same as E[X]². Note also the similarity between the above and the corresponding discrete definition.