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 🙁

**Answer**

If you’ve no mathematical impediments there’s a good overview in Ch. 3 of Casella & Berger, *Statistical Inference*, & much is covered in Grinstead & Snell, *Introduction to Probability* (it’s free); for more detail I’d recommend Severini, *Elements of Distribution Theory*. But there are lots – it would be more difficult, I think, to find a less mathematical treatment that still gives the reader some feel for where different distributions come from.

**Attribution***Source : Link , Question Author : Community , Answer Author : Scortchi – Reinstate Monica*