Moment generating function

Moment generating function
The probability density function (continuous variable) or the probability mass function (discrete variable) of a random variable X contains all the information you'll ever need about this variable.

Although its mean can be taken as zero, since it is symmetrical about zero, the expectation, variance, higher moments, and moment generating function do not exist. The Cauchy distribution is defined as: ...

See also: Distribution, Variance, Demon, Density, Normal distribution