Definition: The t distribution is defined in terms of a normal variable and a chi-squared variable. Let
z~N(0,1) and v~X2(n). (That is, v is drawn from
a chi-squared distribution with n degrees of freedom.)
Then t = z(n/v)1/2 has a t distribution with n
degrees of freedom. The t distribution is a one-parameter family of
distributions. n is that parameter here. The t distribution is symmetric
around zero and asymptotically (as n goes to infinity) approaches the standard
normal distribution.
Mean is zero, and variance is n/(n-2).
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