What Is The Geometric Meaning Of Third Derivative Of A Function At A Point?

What is the actual meaning of "moment" in a moment generating function?

• please establish the distinction between the moments as in physics (dipole moment, moment of inertia, nth moment of area) and in statistcs (raw moment, central moment, nth moment about some point A)

• Answer:

  The distinction is that one is in physics and the other is in probability theory. For any sort of distribution you can calculate moments. The pthpthp^{th} moment is Mp=1∫ρ(x)dx∫xpρ(x)dxMp=1∫ρ(x)dx∫xpρ(x)dxM_p = \frac{1}{\int \rho(x)\,dx} \int x^p\rho(x)\,dx where ρρ\rho is the density of the distribution you're measuring. It doesn't matter whether it's a probability density or physical mass.