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