A.8 Student’s t distribution
X has a Student’s t distribution on ν degrees of freedom, denoted
if it has the same distribution as
where 
and 
are independent, or equivalently if X has density
It follows that if 
are independently 
and
then
The mean and variance are
Because the distribution is symmetrical and unimodal, the median and mode both equal the mean, that is
As the distribution approaches ...
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