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The Max-Boltz equation is ##f=(\frac{m}{2\pi kT})^{3/2}4\pi v^2 exp(\frac{-mv^2}{2kT})##

Apparently the general formula for the average given a statistical function is ##\bar{v}=\int_{0}^{\infty}\frac{fvdv}{n}##

Here is what I don't understand:

1) Where did this formula come from? Does this formula only apply to statistical functions? What is a statistical function?

2) It turns out that division by the number of particles (n) is unnecessary for the Max-Boltz equation. What is reasoning behind this?

3) Why is the integration from zero to infinity? Clearly no particle can have infinite velocity...

Thank you again!