Beta

dist=BetaDistribution[α,β]

PDF[dist,z]

CDF[dist,z]

Manipulate[Plot[PDF[BetaDistribution[α,β],x],{x,0,1},Filling->Axis],{α,1/2,4},{β,1/4,4}]

Manipulate[Plot[Table[PDF[BetaDistribution[α,β],x],{β,{1/4,2,4}}]//Evaluate,{x,0,1},Filling->Axis],{α,1/2,4}]

Manipulate[Plot[Table[PDF[BetaDistribution[α,β],x],{α,{1/2,2,4}}]//Evaluate,{x,0,1},Filling->Axis],{β,1/4,4}]

Mean[dist]

Median[dist]

Variance[dist]

StandardDeviation[dist]

Skewness[dist]

Kurtosis[dist]

CharacteristicFunction[dist,t]

Random[BetaDistribution[1,1]]