Exponential

dist=ExponentialDistribution[λ]

PDF[dist,z]

CDF[dist,z]

Manipulate[Plot[PDF[ExponentialDistribution[λ],x],{x,0,3},Filling->Axis,PlotRange->All],{λ,1/2,2}]

Plot[Table[PDF[ExponentialDistribution[λ],x],{λ,{1/2,1,2}}]//Evaluate,{x,0,3},Filling->Axis,PlotRange->All]

Mean[dist]

Median[dist]

Variance[dist]

StandardDeviation[dist]

Skewness[dist]

Kurtosis[dist]

CharacteristicFunction[dist,t]

Random[ExponentialDistribution[1]]