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Mathematical statistics is the application of mathematics to statistics. Mathematical techniques used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure-theoretic probability theory. Overview. In applying statistics to a problem, it is common practice to start with a population or process to be studied.

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1These notes are meant to supplement the lectures for Stat 411 at UIC given by the author. The course roughly follows the text by Hogg, McKean, and Craig, Introduction to Mathematical Statistics, 7th edition, 2012, henceforth referred to as HMC.

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