Moments and a labelled connection

Integrating x and x² against the density gives E(X)=r/λ and E(X²)=r(r+1)/λ². Therefore variance=r/λ². More generally E(X raised to the power of m ^m)=Γ(r+m)/[Γ(r)λ^m] when the moment exists. A connection added for explanation: setting r=1 gives the exponential density λexp(-λx), mean 1/λ and variance 1/λ². The textbook mentions exponential distribution in an objective but does not provide a substantive exponential lesson in the supplied chapter.