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Unformatted text preview: ator µ: x = xmin +xmax . There could be diﬀerent estimators for the same
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
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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- Spring '08