Stat400lec24 - Statistics 400 Chapter 7 Estimation Maximum likelihood estimates Example If X1 X2 X16 are observations of a random sample of size 16

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Chapter 7 Estimation Maximum likelihood estimates Example: If X1, X2, …, X16 are observations of a random sample of size 16 from a normal distribution N(50,100), Find Blah blah blah How do we know that the mean is 50 and the variance is 100? In this chapter, we consider random variables for which the function form of pdf is known, but of the parameter of the pdf, say θ , is unknown. Parameter space : all possible values of θ . Example: f ( x; θ ) = ( 1/ ) e -x/ 0 < x < θ = { θ :0 < θ < } Objective: Choose one member of as the most likely value of θ How? Take a random sample from the distribution to elicit some information about the unknown parameter of θ X1, X2,…, Xn is a random sample of size n from the distribution x 1 , x 2 ,…, x n are observed values Estimator: The function of X1, X2,…, Xn used to estimate θ , say the statistics u( X1, X2,…, Xn), is called an estimator of θ Fall 2005 - 1 -

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This note was uploaded on 07/24/2008 for the course STAT 400 taught by Professor Tba during the Fall '05 term at University of Illinois at Urbana–Champaign.

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Stat400lec24 - Statistics 400 Chapter 7 Estimation Maximum likelihood estimates Example If X1 X2 X16 are observations of a random sample of size 16

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