07_13 - likelihood estimate for . Def An estimator is said...

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STAT 410 Examples for 07/13/2009 Summer 2009 1. Let X 1 , X 2 , … , X n be a random sample of size n from the distribution with probability density function f ( x ; θ ) = - otherwise 0 1 0 θ 1 θ θ 1 x x 0 < θ < . a) Obtain the method of moments estimator of θ , θ ~ . b) Obtain the maximum likelihood estimator of θ , θ ˆ . c) Suppose n = 3, and x 1 = 0.2, x 2 = 0.3, x 3 = 0.5. Compute the values of the method of moments estimate and the maximum
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Unformatted text preview: likelihood estimate for . Def An estimator is said to be unbiased for if E( ) = for all . d) Is unbiased for ? That is, does E( ) equal ? 2. Let X 1 , X 2 , , X n be a random sample of size n from a population with mean and variance 2 . Show that the sample mean X and the sample variance S 2 are unbiased for and 2 , respectively....
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This note was uploaded on 10/29/2009 for the course STAT 410 taught by Professor Alexeistepanov during the Summer '08 term at University of Illinois at Urbana–Champaign.

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