week2.pdf - Sampling distributions and point estimators By G\u00f6zdem Dural Sel\u00e7uk Definitions \u2022 The random variables X1 X2,\u2026,Xn are a random sample

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Sampling distributions and point estimators By Gözdem Dural Selçuk
Definitions The random variables X 1 , X 2 ,…, X n are a random sample of size n if: a) The X i ‘s are independent random variables. b) Every X i has the same probability distribution. A statistic is any function of the observations in a random sample. The probability distribution of a statistic is called a sampling distribution .
Numerical Summaries of Data Data are the numeric observations of a phenomenon of interest. The totality of all observations is a population . A portion used for analysis is a random sample . We gain an understanding of this collection, possibly massive, by describing it numerically and graphically, usually with the sample data. We describe the collection in terms of shape, outliers, center, and spread (SOCS). The center is measured by the mean. The spread is measured by the variance.
Fig_6-3 Relationship between a population and a sample
Sample Mean