1 ds the distribution of the statistics estimator how

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Unformatted text preview: X is the Maximum Likelihood Estimator for µ in a normal distribution.1 Ds. The distribution of the statistics (estimator) How do we expect X to behave? Ideally , each Xk is exactly µ, so X = µ. 2 How much does X deviate from µ? One proves that 3 ￿ ￿ σ2 2 Xk ∼ N (µ, σ ) are independent , k = 1, . . . , n =⇒ X ∼ N µ, n This is one reason to use X as an estimator of µ for most distributions. See next subsection for another reason. 2 But remember that each Xk has probability zero of being exactly µ. Same for X . 3 This is the Theorem on top of page 221. Part of it is discussed in §4.1.2, see below. The rest — that a sum of ind...
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This note was uploaded on 02/05/2014 for the course MATH 3339 taught by Professor Staff during the Fall '08 term at University of Houston.

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