I am studying the Laplace (Double Exponential) distribution, and I have the following quote from Siegrist, which is quite direct, and not bothered about conditions being fulfilled:
That the odd order moments are 0 follows from the symmetry of the distribution.
However, I have also been know that
So what is applicable here? Is the textbook being informal? Is the odd integral condition not applicable here? If I were to do this properly, would I need to check that the odd improper converged by splitting it at zero, and checking that each one was finite?
I am applying Calculus to probability. The question is not on this specific distribution only, but which ideas are important to retain (when moving from Calculus to Probability).
