Self study on probability and statitistics i know there are similar questions already, but i specifically need a book that covers these topics:


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*Combinatorics, conditional probability, Bayes theorem, random variables, joint probability, probability distributions, Markov Chains, Monte Carlo methods. 


I started with "Understanding Probability" by Henk Tijms but got a little frustrated along the way, because the author gives too much for granted. Should i keep using this book or can you suggest something better?
Thank you.
 A: I full-heartedly recommend Introduction to Mathematical Statistics by Hogg, Craig and McKean, 7th edition. My professors have led to believe that this is the mainstream text for a first course in mathematical statistics.
It covers all your desired topics and has strong emphasis on monte carlo simulations via R. It teaches you how to write good R-code and gives you sample algorithms for you to work out, e.g. the empirical significance of a t-test and many more. You will be surprised by how much you can accomplish with R.
All in all, it is considered an intermediate statistics textbook and it does not have many analysis prerequisites. Those things you need to know are discussed in the appendix and it's really elementary, for example the squeeze theorem. Look it up.
A: A First Course in Probability by Sheldon Ross covers all of those, with the possible exception of Monte Carlo (it isn't in the 9 chapters i've gone through, and it isn't in the title of any subsequent section).  
The book is what i'd consider detailed, especially with regards to having many well-elaborated example problems.  Additionally, if you ever get stuck with the exercises, the solutions are all online, often with more than one source available (ie chegg and the following:  http://math.gmu.edu/~dsingman/351/weatherwax2012.pdf ). 
A: I found A First Course in Probability by Sheldon Ross good. It assumes you have a basic knowledge of calculus.
A: You may want to try this out too (although it's not a book) 
https://www.edx.org/course/mitx/mitx-6-041x-introduction-probability-1296
