Statistics Homework Solutions 101

Statistics Homework Solutions 101 - 101 SECTION 4.10 ¢ is...

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Unformatted text preview: 101 SECTION 4.10 ¢ is therefore e λ λ e ¡ ¡ ¡ X. Xn is The joint probability density function of X1 n 2 2 n 2 2 1 f x1 xn ; σ ∏ σ 2π e xi 2σ 2π n 2σ n e ∑i 1 xi 2σ . i1 The MLE is the value of σ that maximizes f x1 xn ; σ , or equivalently, ln f x1 ¨¨¨  ¥ ¡ ¤ ¨¨¨  ¤ ¡ ¡ ¥ £¤ ¡ ¡¥ ¨¨¨  ¤ ¡ ¡ ¢ ¡ ¢ ¡ ¡ ¡ (c) Yes ¡ (b) No 1. (a) No ¡ Section 4.10 ∑n 1 Xi2 i . n ¢ ¤ The MLE of σ is σ ¡ ¡¥ ∑n 1 x2 i i n ¡ ¦ ¡ σ ∑n 1 x2 i i n ¢ ¤ σ2 n σ ∑n 1 x2 i i σ3 ¡ ¥ Now we solve for σ: n ∑ n 1 x2 i i 0 σ σ3 nσ2 ∑n 1 x2 0 i i x2 ¨¨¨  i1 ¤ n i ∑ 2σ2  ¨ ¨  ¨ n ln σ 0. xn ; σ . ¥ ¦ n 2 ln2π d dσ xn ; σ d ln f x1 dσ ¦ 7. X . The MLE of e (c) The MLE of λ is λ ...
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This note was uploaded on 12/20/2011 for the course STA 3163 taught by Professor Mattgilg during the Fall '11 term at UNF.

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