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Unformatted text preview: Introduction to Estimation Data arise from measurements whose values depend on characteristics of the process or ex periment being considered. Some features of the process can be controlled while others can not and result in variation in the data. If we could make many observations { x 1 ,x 2 ,...,x N } under similar circumstances, then this collec tion would tell us everything about the under lying process. The collection would be best described by its histogram. The centre of the histogram would give the mean and the spread would indicate how much variation there is. 1 Examples • Department store wants to know the pro portion p of females between 18 and 25 who have a credit card. Takes random sample. • Manufacturer is interested in proportion p of defective parts in an inventory of 100,000 parts. Collect data by taking measure ments. • Manufacturer is interested in mean break ing strength μ of steel beams produced with specified percentages of raw material. Takes a random sample. 2 In each case above, there is a population of interest (that is a distribution) and a charac teristic of the population ) the p or μ , which are unknown. Such a characteristic is called a parameter and generically denoted by the sym bol θ. Data are collected in order to learn about θ. From the data or sample, a guess, called an...
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 Fall '10
 drera

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