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I have Ross a First Course on Probability and Bertsekas Introduction to probability book. However these two books do not exactly give me what I am looking for.

The problem is Bertsekas book is introductory while Ross book explains expression $E[\ E[X\mid Y] \ ]$ just by briefly saying it is a function of $y$ if I remeber correctly.

I need a probability book which will make me feel comfortable with the symbols and letters rather than ready made formulas. I want to be able grasp when a random variable is a constant or when it is not. I want to be able to read and understand equations involving both random variables and constants and when are interpreted as a rv. when they are not etc.

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Try Probability with martingales by Williams – Ilya Jan 11 '13 at 20:43
You used the letter (capital) $Y$ to refer presumably to a random variable, then you used the letter (lower-case) $y$, and it's not clear to me what you mean by it. – Michael Hardy Jan 11 '13 at 21:01
Try the course notes here which have replaced Ross's book as the text for an undergraduate course in probability. Incidentally, I doubt very much that Ross says anywhere that $E[E[X|Y]]$ is a function of $y$; he does point out that the expected value $E[X|Y = y]$ can be regarded as a random variable, denoted $E[X|Y]$, since it depends on our choice of the value $y$ that $Y$ took on; and so $E[X|Y]$ is a function of $Y$. – Dilip Sarwate Jan 11 '13 at 21:46

If you want to truly understand the mathematical foundations try first learning a bit of measure theory. A probability space is a special kind of measure space and a random variable is a measurable function. Measure theory is not easy but there are several sources. Folland's book on analysis has a chapter on probability theory and Tao's recent book also related measure theory to probability.

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Give Bruce Hajek's notes on Random Processes a try. I found some of the diagrams pretty intuitive and easy to understand even if you are a novice or not. See a snippet from his notes below: enter image description here

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Bruce Hajek's notes referred to are for a graduate course in probability theory. The OP will be better served by the more elementary version for Bruce's undergraduate course. – Dilip Sarwate Jan 11 '13 at 21:41
@Dilip Thanks for the link. I hope that is helpful as well to OP. – jay-sun Jan 11 '13 at 21:59
why the down vote? :) – jay-sun Feb 26 '13 at 17:38
I did not down-vote your answer, someone else did. – Dilip Sarwate Feb 27 '13 at 0:17
@DilipSarwate I didn't say you did. Don't care actually. – jay-sun Feb 27 '13 at 0:31

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