x̄ - > Mean Zipf distribution, rho=2

mean Zipf distribution, rho=2

mean | Zipf distribution | parameter | ρ = 2

π^2/(6 ζ(3))≈1.36843

mean | π^2/(6 ζ(3))≈1.36843

standard deviation | ∞

variance | ∞

skewness | ∞

kurtosis | ∞

P (X = x) = piecewise | 1/(x^3 ζ(3)) | x>=1

0 | (otherwise)

Plot of CDF

P (X<=x) = piecewise | H_floor(x)^(3)/ζ(3) | x>=1

0 | (otherwise)

Plot of CDF