is a sample of size N drawn from a normal distribution with mean E(X) and variance 
, then 
and
are estimators of the mean E(X) and of the variance of the estimator 
. The quotient
is described by Student's distribution (also called the t-distribution) with f=N-1 degrees of freedom. Its probability density is
where 
denotes Euler's gamma function. The t-distribution has the properties
For 
it approaches the standard normal distribution.