slide2 - ! The 20% trimmed mean X X ~ ) 20 ( tr X 5 Example...

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1 Random Sampling ! Population ! Random sample: ! Independent variables ! Same probability distribution ! Statistics ! Point estimate 2 Examples ! Mean of a single population ! Variance of a single population ! Difference in means of two population µ 2 σ 2 1 µ µ
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3 Unbiasedness ! An estimator Θ of some unknown quantity θ is said to be unbiased if the procedure that yields Θ has the property that, were it used repeatedly the long-term average of these estimates would be θ . ! That is to say, E( Θ ) = θ . 4 Example 1 ! Given X = (5.8, 4.4, 8.7, 7.6, 3.1) ! The Sample Mean ! The Sample Median
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Unformatted text preview: ! The 20% trimmed mean X X ~ ) 20 ( tr X 5 Example 2 ! Sample Variance ! Expectation of Sample Variance 1 n ) X X ( S n 1 i 2 i 2 = = 2 2 ) S ( E = 6 Variance of a Point Estimator ! MVUE Smallest variance estimator ! Theorem If X 1 ,X n is a random sample of size n form a normal distribution with mean and variance , then the sample mean is the MVUE for 2 X 7 Example 1 (continued) n 6 . ) X ( V 2 ) 20 ( tr = 2 ) X ~ ( V = n ) X ( V 2 =...
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This note was uploaded on 05/05/2008 for the course IE 121 taught by Professor Perevalov during the Spring '08 term at Lehigh University .

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slide2 - ! The 20% trimmed mean X X ~ ) 20 ( tr X 5 Example...

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