1. Probability Density Functions

What is the limiting behavior of such function where we find behavior of these functions at infinity towards 0?

What is the limiting behavior of such functions?

Does it have to go to zero?

What are the different sorts of behaviors of PDF's?

2. Moments

In engineering measurements are of finite range. In that case how does this effect moments?

Moments sometimes does not exist like Koshy distribution groups. How does this relate to this idea of finite dynamic range?

Is the Koshy distribution physically relevant if the moments do not exist?

3. Bayes Theorem

Why some people are Bayesian, and some people are not?

Is Bayes theorem correct? Or it needs some specific restrictions to be true?

As an engineer when would you apply bayes theorem?

Are engineering Bayesians?