Book recommendations for beginners about probability distributions I'm studying machine learning and every book I open I bump into chi-squared distribution, gamma-function, t-distribution, Gaussian, etc.
Every book I have opened so far only defines what the distributions are: they don't explain or give the intuition on where the specific formulas for the functions come from.
For example, why is chi-squared distribution the way it is? What is the t-distribution? What is the intuition behind the distribution? Proofs? etc.
I would like to have a clear and fundamental understanding of the most commonly used distributions so that every time later on when I see them, I truly understand what is a t-distribution, what is a Gaussian distribution and most importantly why are they the way they are.
It would be nice if the books / tutorials can explain the concepts to a layman so that in order to understand them you don't already need to understand them x) Many books are like this, they don't fit for beginners

I am not familiar with any book that would meet your requirements, but there's a Harvard course Statistics 110 by Joe Blitzstein that focuses exactly on the intuitions behind the distributions and probability theory concepts. (It is freely available online.)
