StudentT

dist=StudentTDistribution[n]

PDF[dist,z]

CDF[dist,z]

Manipulate[Plot[PDF[StudentTDistribution[n],x],{x,-5,5},Filling->Axis],{n,0.1,4}]

Plot[Table[PDF[StudentTDistribution[ν],x],{ν,{0.1,0.5,4}}]//Evaluate,{x,-5,5},Filling->Axis]

Mean[dist]

Median[dist]

Variance[dist]

StandardDeviation[dist]

Skewness[dist]

Kurtosis[dist]

CharacteristicFunction[dist,t]

Random[StudentTDistribution[1]]