Chapter 5.1-5.2 - Math3200 Intermediate Probability and Statistics Prof Nan Lin Department of Mathematics Washington University Populations Samples

# Chapter 5.1-5.2 - Math3200 Intermediate Probability and...

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Math3200 Intermediate Probability and Statistics Prof. Nan Lin Department of Mathematics Washington University

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Populations, Samples, Parameters, and Statistics
Outline Sampling distribution of the sample mean Central limit theorem Normal approximation of binomial Continuity correction Sampling distribution of the sample mean Chi-square distribution

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What we learned before ? = 1 𝑛 ? 𝑖 𝑛 𝑖=1 If ? ? 𝑖 = ? 𝑖 , ? ? = 1 𝑛 ? 𝑖 𝑛 𝑖=1 If ??𝑟 ? 𝑖 = 𝜎 𝑖 2 and ? 𝑖 are mutually independent, ??𝑟 ? = 1 ? 2 𝜎 𝑖 2 𝑛 𝑖=1 If ? 𝑖 are mutually independent with mean ? ? 𝑖 = ? and ??𝑟 ? 𝑖 = 𝜎 2 , ? ? = ?, ??𝑟 ? = 𝜎 2 ? If ? 𝑖 are i.i.d. 𝑁(?, 𝜎 2 ) ? = 1 ? ? 𝑖 𝑛 𝑖=1 ~𝑁(?, 𝜎 2 ? )