To give you a little context, I study for a master's degree on statistics and probability. I was never top in my class and I managed to get decent grades with as little work as possible. While writing my bachelor's thesis, I worked a little bit more on understanding a specific problem my professor gave me, and proved a small result regarding ramification chains using measure theory. It made a positive impression and got me fairly easy admitted to the master's programme. Now during my exams I realise I lack knowledge and experience regarding problem solving due to my laziness. I developed real interest in mathematics and I wish to improve at problem solving ( both theoretical and practical ).
I am looking for books concerned with problems and applications and that also provide explanation and/or solutions to them. It would be great to also point out theory that is needed not necessarily explaining it. The topics I am interested in are real analysis, probability and statistics. I believe those are fairly connected and I am looking for a mix of problems to gradually improve my understanding.
It should start fairly easy and get to decent or even hard problems. It should cover most common concepts.
I thank you for your time!
P.S: I had an exam in an introductory course on statistics and almost failed miserably because even though I knew what expectation of a random variable was, I could not compute it since I did not have any relevant experience with series.
Best Answer
Suggestion: A Problem Book in Real Analysis.