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I want to improve my knoweldge of statistics (part pleasure, part work) and have been recommended 'Statistical Inference' by Casella and Berger as a good foundation text at the undergraduate level (also 'Probability and Random Processes' by Grimmett and Stirzaker).

I graduated in science, not mathematics, and feel it assumes a level of maths I don't have, for example, on sigma algebra the line "...it follows that B is closed under countable intersections." really threw me as I've not encountered the term before. That aside, a lot of the probability I've skimmed through looks familiar so I don't think I'm too far off the start line.

Are there any maths subjects, even at the high school level, that are worth revising/learning before working through this book? My calculus is OK, so I'm guessing something on sets? Any help would be greatly appreciated.

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  • $\begingroup$ Grimmett is actually a really good book on probability which covers the necessary background set theory and the like. I might recommend reading up to about Chapter 7 in Grimmet before doing Casella and Berger. The nice thing is it’s a book about probability not about all of the machinery needed to eventually do probability, so it’s more beginner friendly than something that throws sigma algebras at you paragraph one. $\endgroup$
    – eepperly16
    Commented Jun 5, 2019 at 5:49
  • $\begingroup$ Thanks @eepperly16. Is there another branch of maths that gives a more gentle introduction to sigma algebras? It feels like I'm missing a tool box to understand them. I've got both books so I'll follow your advice. $\endgroup$
    – Matt N
    Commented Jun 5, 2019 at 6:03
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    $\begingroup$ The other big area of math which uses $\sigma$-algebras is graduate-level real analysis, and that is certainly not going to be a more gentle introduction than you'll find in Grimmet. To supplement, here is a good general reference for sets and functions and stuff (the section on proofs earlier is also good.) It's where I learned most of this stuff. $\endgroup$
    – eepperly16
    Commented Jun 5, 2019 at 6:26
  • $\begingroup$ Thank you so much @eepperly16, thats helped me so much! $\endgroup$
    – Matt N
    Commented Jun 5, 2019 at 8:50

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This is a text for Master's students. DON'T use this as your first introduction to Statistics. PreRequisites are

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    Commented Oct 3, 2023 at 23:04

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