When trying to understand the moment-generating function, I've stumbled upon this general function:
Mx(t) = E[e^tx], t ∈ R
I understand that you have X = (X1, ... Xn) a series of random variables and that you draw a vector through tX.
It may sounds naive, but why use the exponential of that series? Why not ln for instance? After all, both are monotonous, continuous, positive on R? (and are also closely connected, though ln is much slower than e).
Thank you very much for your insights!