Let XXX have the Pareto distribution with PDF f(x)=αxmαxα+1f(x) = \frac{\alpha x_m^\alpha}{x^{\alpha+1}}f(x)=xα+1αxmα for x≥xmx \geq x_mx≥xm. What is the mean?
αxmα−1\frac{\alpha x_m}{\alpha-1}α−1αxm for α>1\alpha > 1α>1
αxmα+1\frac{\alpha x_m}{\alpha+1}α+1αxm for all α\alphaα
xmα\frac{x_m}{\alpha}αxm
Undefined for all α\alphaα