How do you derive mean of Pareto distribution?

You must know calculus, at least that the integral of x N 1/(N+1)x N+1 Define the Pareto distribution as: f(x) = ab a x (a+1) or Cx (a+1) where C = ab a (a constant) Remember that the pdf is defined over the domain b, inf otherwise zero Mean = integral xf(x) evaluated from be to infinity Remember also that the limit of 1/x as x goes to infinity = 0. Similarly for any positive a, (1/x) a goes to 0 as x goes to infinity mean = integral C x (a+1) x dx = integral Cx a C(1/(-a+1))x a+1 evaluated over the interval be to infinity The integral is zero at infinity, so the mean = C(0-1/(-a+1))b a+1 Remember be a+1 be a be After substituting and cancelling mean = ab/(a-1) for a greater than 1.

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