Unformatted text preview: with mean μ and variance σ 2 . (a) Use Slutzky’s theorem to show that √ n ( Xμ ) 2 p → 0 as n → ∞ . (b) Use (a) to show that √ n ( S 2 nσ 2 ) D → N (0 , γ 4 ) as n → ∞ , where γ 4 = E( X 1μ ) 4σ 4 . 3. Let X 1 , . . ., X n ∼ iid Beta( θ, 1) , θ > , i.e. their common pdF is f ( x ) = θ x θ1 , x ∈ [0 , 1] . (a) Show that h θ = X 1X is a method oF moment estimator oF θ . (b) ±ind the large sample distribution oF √ n ( θθ ) . (HINT: Use the δmethod.)...
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 Spring '07
 Polonik
 Statistics, Normal Distribution, Let X1

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