The Short question: Where can I find a book for probability and statistics book that teaches them from scratch in a rigorous (very important condition) way ? The book must not be elementary, but it has to start from scratch.( For example, I think Lang/Hungerford algebra begin by defining what a group is, in that sense they start from scratch.)

The long question: I only took an engineering course in probability and statistics. In my opinion, it is very louzy/non-rigorous. You may assume, I have no knowledge of probability and statistics. I have to take an independent study statistics course this year. I am allowed to choose a book for the course. It has to be a statistics course. My instructor assumes I know probability because I took the course mentioned above.( I admit I have a poor understanding of probability and this irritates me a lot) . I'd like ato have a book that is:

1) Rigorous

2) It has a significant statistics part

3)It teaches the amount of probability needed to to do statistics


You might want to look at Statistical Inference by George Casella and Roger L. Berger. It's the book I used for my graduate inference class.


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