There could be dierent estimators for the same 2

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Unformatted text preview: ator µ: x = xmin +xmax . There could be different estimators for the same ˜ 2 population parameter. Choosing between them is a part of statistics. For now, trust me x is “better” than x . ¯ ˜ Another population parameter one might be interested and its estimator: σ 2 and s2 = 3 (xi −x )2 ¯ n−1 . Yet another population parameter: Say you are wondering the proportion of the left no of lh in pop handed people in the population. Let’s call it p = . An estimator for N no of lh in the sample p could be p = n Utku Suleymanoglu (UMich) Sampling Distributions 6 / 21 Sampling Distributions Estimators as Random Variables Estimators are formulas or rules which uses sample values in them. They take different values for different samples for the same variable from same population. Different estimates . . . If we randomly pick samples from a populations, then the outcome of the estimator formula is random. Therefore, estimators are random variables. What do random variables have? distributions, means and variances . . . For a given estimator, such as x , we can figure out what the mean and t...
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