I went to listen to a workshop and someone from the audience asked the presenter how the moments can improve the [mutual information](https://en.wikipedia.org/wiki/Mutual_information). I am learning about MI (Mutual Information) so didn't have enough knowledge to understand what it means. Then, I did some research but I still have some confusion. I am wondering if someone who has more knowledge about this can clarify things for me. Here are my questions:

 - Mutual information is usually calculated by bin functions to estimate the probability of two random variables which can be a case of two vectors $X$ and $Y$. Is the moment generating function another way to estimate probability?

 - If moment generating functions can present the probability of $X$ and $Y$, how do we calculate it? 

 - Does a MI have a moment generating function?

 - If MI has a moment generating function, how can we present a MI of $X$ and $Y$ by its moment functions?