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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

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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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