1

I just finished a course in probability theory in my undergrad but I felt that it lacked some things. So I'm looking for a good probability theory book for a second approach. One of the things the course lacked was a motivation for any of the definitions for the random variables. Especially the normal distribution. I have no idea why the curve is defined the way it is. So a book that went into the motivation and properties and applications of specific random variables would be great. It would also be nice if the book had a good measure theoretical basis, not some thing to in-depth, I have read some measure theory from Rudin. I know that both applied and measure theory might be too much to ask for from one book, so I value more the applied side.

BENG
  • 1,239
  • Typically the measure theoretic books do not go into motivations of specific distributions but I highly recommend Feller’s volume 1 for derivations and motivations and a huge variety of examples of distributions in science and D. Williams Probability with Martingales for more measure theoretic treatment. – Nap D. Lover May 04 '20 at 22:56
  • The best book in probability theory ever written is Ash's "Real Analysis and Probability." However, he will not see any probability before chapter 5 and up to that point the book will be heavy in analysis (in locally compact, metrisable spaces; some may say that he sees "functional analysis" in lieu of "analysis" whatever these terms mean). – William M. May 04 '20 at 22:56
  • @NapD.Lover I think I remember reading in the intro of Feller that continuous distributions are left for the second volume is that true? or is there stuff like normal and exponential distributions in volume one – BENG May 04 '20 at 23:06
  • You are correct, continuous random variables proper are treated in the second volume and a little measure theory is also indicated there too. However, the normal distribution is introduced in the first volume multiple times due to the CLTs for binomial and Poisson RVs, and if I recall correctly, in the chapters on random walks too. Your mileage may very, so to speak. By the way, for just the derivation of the normal distribution, you may want to check out e.g. https://math.stackexchange.com/questions/384893/how-was-the-normal-distribution-derived – Nap D. Lover May 04 '20 at 23:18

0 Answers0