A statistical distribution published by William Gosset in 1908. His employer, Guinness Breweries, required him to publish under a pseudonym, so he chose "Student." Given 
independent measurements 
, let
independent measurements , let  | (1) |
where 
is the population mean, 
is the sample mean, and 
is the estimator for population standard deviation (i.e., the sample variance) defined by
is the population mean, is the sample mean, and is the estimator for population standard deviation (i.e., the sample variance) defined by  | (2) |
Student's 
-distribution is defined as the distribution of the random variable 
which is (very loosely) the "best" that we can do not knowing 
.
-distribution is defined as the distribution of the random variable which is (very loosely) the "best" that we can do not knowing . The Student's 
-distribution with 
degrees of freedom is implemented in Mathematica as StudentTDistribution[n].
-distribution with degrees of freedom is implemented in Mathematica as StudentTDistribution[n]. 
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