Polya-Aeppli geometric-Poisson distribution moment properties
PolyaAeppliDistribution[θ, p]
Mean[PolyaAeppliDistribution[θ, p]]
→ θ/(1 - p)Variance[PolyaAeppliDistribution[θ, p]]
→ ((1 + p)*θ)/(1 - p)^2DiscretePlot[Table[CDF[PolyaAeppliDistribution[7, p], x], {p, {0.2, 0.4, 0.6}}]//Evaluate, {x, 0, 35}, ExtentSize -> Right]
→ -Graphics-