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Some x estimate we have say 2154 is not exactly but it

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Unformatted text preview: x estimates, the average of these diﬀerent x ’s will ¯ ¯ tend to µ as we get more and more samples and produce estimates. → Some x estimate we have, say 21.54 is not exactly µ, but it is the best we can do with ¯ one single sample. What we know is: the way we form our estimate is good. In general, a point estimator whose mean equals the population parameter is called an unbiased estimator. X is an unbiased estimator of µ. We will come back to this. Utku Suleymanoglu (UMich) Sampling Distributions 10 / 21 Sampling Distributions Variance of X n Again, starting from X = i =1 Xi = X1 +X2 +···+Xn , we can take the variance of X . Note n n that there is no covariance term, because random sampling ensures covariance is zero. X1 + X2 + · · · + Xn ) n 1 1 1 = V ( X1 + X2 + · · · + Xn ) n n n 1 = 2 V (X1 + X2 + · · · + Xn ) n 1 = 2 (V (X1 ) + V (X2 ) + · · · + V (Xn )) n 1 = 2 (σ 2 + σ 2 + · · · + σ 2 ) n 1 σ2 = 2 (n × σ 2 ) = n n 2 σx = V (X ) = V ( σx = ¯ σ √ n is called the standard e...
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This note was uploaded on 03/17/2014 for the course ECON 404 taught by Professor Staff during the Spring '08 term at University of Michigan.

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