I recently finished studying a book in elementary probability theory. I am particularly interested in continuous probability distributions, but since the book was just an introduction to probability theory it didn't cover those to a satisfactory extent. I never really got to put anything I learned to use other than solving a couple of basic assignments. If I want to learn more about continuous distributions, what book should I pick? I haven't had statistics yet, would that perhaps the be correct choice? Is there perhaps some book in differential equations that is centered around probability theory?
A question regarding further studies of continuous probability distributions
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1How much measure theory do you know? Measure theory is foundational to probability theory in its full generality. – 2017-01-05
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0I've had none thus far. – 2017-01-05
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0Then I suggest looking up Fremlin's Measure Theory. The text is gratuitously thorough (a feature well suited to self-study imho). It discusses measure theory in its full generality, but the subject of probability measures is covered in detail, like everything else measure theory. – 2017-01-05
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0I will look it up, thank you. – 2017-01-05
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2What is to a satisfactory extent? Measure theory is overkill for someone who just wants to learn a bit of probability. Especially something like Fremlin -- most measure theoretic intro probability texts have sections on measure theory which are more than sufficient if you choose to go down that route (e.g. Durrett). – 2017-01-05
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1what book did you finish and what other background do you have? What are you hoping to learn about continuous distributions? Are you looking for more rigor? It's unclear if the next step is measure-theoretic probability or something where you're learning to do gaussian integrals and marginalize out variables in pdfs, etc – 2017-01-05
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0@spaceisdarkgreen For probability I studied "A first course in probability" by Sheldon Ross. In addition to that I've had single variable and multivariable calculus, real analysis, some very very basic linear algebra and bit of ODE's. I'm looking to study distribution functions more in-depth and joint relationships between continuous random variables. – 2017-01-05
1 Answers
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Grinstead and Snell's book is available in printed form or as a free PDF provided by the authors.
A book I have used for undergraduate post-calculus courses in probability is Wackerly et al.: Math Stat with Applications. I think the probability chapters would be good for self study. Many editions, older ones should be OK for your purposes and cheaper. Many answers at the back of the book. Maybe you could find a student solutions manual that matches one of the editions.
Other popular books at about the same level include those by Ross and by Hogg & Craig. Also calculus prereq, but maybe not so good for self-study. There are dozens of books. I am just mentioning ones I have seen students use.
At your level, I don't see a direct connection to differential equations (unless maybe a course in that would sharpen up your calculus). It sounds as if you may be interested in applications, so you may get into motivating material earlier if you start at the basic calculus level now, and leave the measure theoretic treatment until later.
If you are still at or near a college or university with a reasonably strong program in probability and statistics, maybe you can find a faculty member willing to find out more about your background and interests who can give you personal advice.