Population Mean

The mean of a distribution with probability density function  is the first raw moment , defined by

(1)

where  is the expectation value.

For a continuous distribution function, the population mean is given by

(2)

where  is the expectation value. Similarly, for a discrete distribution,

(3)

The population mean of a distribution is implemented in the Wolfram Language as Mean[dist].

The sample mean is an unbiased estimator for the population mean.