HW6 - 7-29. f ( x) = e x! - x L ( ) = i =1 n e e = xi ! xi...

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7-29. ! ) ( x e x f x λ = = = = = = n i i i x n n i i x x e x e L n i i 1 1 ! ! ) ( 1 n x n x x n x n d L d x x e n L n i i n i i n i i n i i n i i n i i = = = = = = = = = + = + = + = 1 1 1 1 1 1 ˆ 0 0 1 ) ( ln ! ln ln ln ) ( ln 7-35 a) = = = n i i X n X E 1 2 2 1 2 ) ( θ so = = n i i X n 1 2 2 1 ˆ Θ b) ∑∑ = = = = n x L n x x L e x L i n i i i x i i 2 2 1 2 2 2 1 ) ( ln ln 2 ) ln( ) ( ln ) ( 2 Setting the last equation equal to zero, the maximum likelihood estimate is = = n i i X n 1 2 2 1 ˆ and this is the same result obtained in part (a) c) ) 2 ln( 2 ) 5 . 0 ln( 2 1 5 . 0 ) ( 0 2 / 2 = = = = a e dx x f a a We can estimate the median ( a ) by substituting our estimate for θ into the equation for a . d) 4.809167 2 1 ˆ 1 2 = = Θ = n i i X n , so 4.809167 / 2 4.809167 ) ( x e x x f = . The proportion of individuals with incomes less than $45,000 is 0.8781975 4.809167 ) ( 5 . 4 0 4.809167 / 5 . 4 0 2 = = dx e x dx x f x
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8-1 a) The confidence level for n x n x / 14 . 2 / 14 . 2 σ μ + is determined by the value of z 0 which is 2.14. From Table III, Φ (2.14) = P(Z<2.14) = 0.9838 and the confidence level is 2(0.9838-0.5) = 96.76%.
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This note was uploaded on 05/05/2010 for the course STAT 601 taught by Professor Wherly during the Spring '08 term at Texas A&M.

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HW6 - 7-29. f ( x) = e x! - x L ( ) = i =1 n e e = xi ! xi...

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