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Mathematical Statistics With Applications - 7 Edition - Chapter 9 - Problem 9.2
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# Let Y1, Y2,..., Yn denote a random sample from a population with mean and variance 2

Mathematical Statistics with Applications | 7th Edition

Problem 9.2

Let Y1, Y2,..., Yn denote a random sample from a population with mean and variance 2. Consider the following three estimators for : 1 = 1 2 (Y1 + Y2), 2 = 1 4 Y1 + Y2 ++ Yn1 2(n 2) + 1 4 Yn , 3 = Y . a Show that each of the three estimators is unbiased. b Find the efficiency of 3 relative to 2 and 1, respectively.

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Stat notes 2 Categorical data= nominal and ordinal Quantitative data= discrete and continuous Relative frequency table- all #’s in table sum to 1 for percentages Proportion= # in category/ total sample size (risk is the same thing as proportion) How do you know which variable is the response and which is the explanatory Rows= response variable Columns= explanatory variable How do we compare the risks of two different groups By using relative risk - If relative risk is less than, first group has a smaller risk - Odds- ratio of counts of the two levels of one categorical variable  haves/have nots Proportion for a sample- p (hat) Proportion for population- P Two-way table- used to show the relationship between two categorical variables Two categorical variables: -

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Let Y1, Y2,..., Yn denote a random sample from a population with mean and variance 2