Statistics/Distributions/Studentt
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< Statistics  Distributions
Studentt Distribution[edit]
Probability density function 

Cumulative distribution function 

Parameters  ν > 0 degrees of freedom (real) 

Support  x ∈ (−∞; +∞) 
CDF  where _{2}F_{1} is the hypergeometric function 
Mean  0 for ν > 1, otherwise undefined 
Median  0 
Mode  0 
Variance  for ν > 2, ∞ for 1 < ν ≤ 2, otherwise undefined 
Skewness  0 for ν > 3, otherwise undefined 
Ex. kurtosis  for ν > 4, ∞ for 2 < ν ≤ 4, otherwise undefined 
Entropy  ... 
MGF  undefined 
CF  for ν > 0

Student tdistribution (or just tdistribution for short) is derived from the chisquare and normal distributions. We divide the standard normally distributed value of one variable over the root of a chisquare value over its r degrees of freedom. Mathematically, this appears as:
where and .