# 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 :(

• Most undergraduate texts on theoretical statistics or probability theory have a chapter on distribution theory that covers these questions. But how much mathematical background would you want to assume? – Scortchi - Reinstate Monica Jul 2 '13 at 10:05
• undergraduate mathematical background :) The fundamental building blocks. Is that sufficient? What kind of level of mathematics should I acquire before learning about the distributions? I have read a basic book about statistics, which only shortly presented the distributions I described in the question. – jjepsuomi Jul 2 '13 at 10:07
• Some probability theory & calculus ought to do it - it depends how deep you want to go. – Scortchi - Reinstate Monica Jul 2 '13 at 11:35
• Okay, thank you :) Mostly I'd just want to understand what I'm doing – jjepsuomi Jul 2 '13 at 11:48
• You also might find useful the references posted in this thread: stats.stackexchange.com/questions/56385/…. – Andre Silva Jul 2 '13 at 13:02