What Book Best Explains the Distribution of Combined Random Variables?

[pabl012]

Hello everyone.
Recently I've been working in a project involving some statistics, and I've found that I lack knowledge about this.
So I'm looking for a book about probability and statistics, but I'm specially interested in how one can get the distribution of a combination of others distributions.
I know that if X and Y are random variables then one can calculate the characteristic function, and multiply... to get the distribution of Z = X + Y. I am not interested on this; I am not interested in the results as much as I am interested in how to arrive to them.
I'm looking for a book that explain how to think in problems like combine (X^2 + Y)/Z with X,Y,Z random variables, and why the operations are done like they are done. Starting with the simplest and continuing with increasingly serious things. With proofs of the theorems, and, if possible, been simple (that not easy) and elegant.
I would like to find something like the "Complex Variables with Applications" of A. David Wunsch, but with probability and statistics.

Sorry if I can't explain better and thanks in advance.

P.D.: I'm physicist, so I'm not afraid of serious business.

 

[Stephen Tashi]

In looking for such a book myself, the title "The Algebra Of Random Variables" by Melvin Springer comes up, but I've never been able to find a copy of it. (A review of the book: http://www.ams.org/journals/bull/1980-02-01/S0273-0979-1980-14729-1/S0273-0979-1980-14729-1.pdf ).

 

[pabl012]

That seems to be my title, but when I searching in Google, I just found the amazon one, and costs 1000$!
Does anyone have a copy of the book, or knows a title of the same features?

Thanks