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Chapter 8 Homework 2: Principles of Data Reduction: Problems and Solutions | STAT 205B: Classical Inference

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This is my E-version notes of the classical inference class in UCSC by Prof. Bruno Sanso, Winter 2020. This notes will mainly contain lecture notes, relevant extra materials (proofs, examples, etc.), as well as solution to selected problems, in my style. The notes will be ordered by time. The goal is to summarize all relevant materials and make them easily accessible in future.

Chapter 8 Homework 2: Principles of Data Reduction: Problems and Solutions | STAT 205B: Classical Inference STAT 205B: Classical Inference Chapter 8 Homework 2: Principles of Data Reduction: Problems and Solutions Exercise 8.1 (Casella and Berger 6.1) Let \(X\) be one observation from a \(N(0,\sigma^2)\) population. Is \(|X|\) a sufficient statistic? Proof. Consider the pdf given by \[\begin{equation} f(x|\sigma^2)=(2\pi\sigma^2)^{-1/2}exp(-\frac{x^2}{2\sigma^2}) =(2\pi\sigma^2)^{-1/2}exp(-\frac{|x|^2}{2\sigma^2}) \tag{8.1} \end{equation}\] Define \(g(t|\sigma^2)=(2\pi\sigma^2)^{-1/2}exp(-\fra

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