User talk:Asweatherbee/sandbox

Hello - I have noticed what I think to be an inconsistency in the article. The second sentence reads:

If a random variable admits a probability density function, then the characteristic function is the inverse Fourier transform of the probability density function.

and then, at the end of the Introduction section, there is this sentence:

Note however that the characteristic function of a distribution always exists, even when the probability density function or moment-generating function do not.

I believe these two sentences are inconsistent. Since it is stated in the first sentence that the characteristic function in the inverse FT of the PDF, and then in the second sentence it is claiming that the PDF doesn't even need to exist.

This is confusing. I am not an expert, but believe that one who is needs to clarify this.