3044hw5s09sols

3044hw5s09sols - 2 ISyE 3044/Spring 2009/Solutions to...

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Unformatted text preview: 2 ISyE 3044/Spring 2009/Solutions to Homework #5 1. (a) We have Z 1 = radicalBig − 2 ln(0 . 82) cos[2 π (0 . 40)] = − . 013 , Z 2 = radicalBig − 2 ln(0 . 82) sin[2 π (0 . 40)] = 0 . 37 . (b) N = min { k ≥ 1 : producttext k +1 i =1 U i < e- 5 = 0 . 0067 } = 8. (c) The c.d.f. is F ( x ) = integraltext x 2(1 − t ) dt = x (2 − x ), 0 ≤ x ≤ 1. Solving the 2nd-degree equation X (2 − X ) = U , we get X = 1 − √ 1 − U . 2. ExpertFit recommends various models including the gamma and Weibull ones. The best fit appears to be the gamma(E) model with a location parameter of 10. 3. (b) First sort the observations from smallest to largest: X (1) ≤ ··· ≤ X (5) . Using ˆ F ( x ) = 1 − e- (0 . 2 x ) 2 we compute the test statistic D = max braceleftbigg max 1 ≤ i ≤ 5 bracketleftbigg i 5 − ˆ F ( X ( i ) ) bracketrightbigg , max 1 ≤ i ≤ 5 bracketleftbigg ˆ F ( X ( i ) ) − i − 1 5 bracketrightbiggbracerightbigg = max { , . 599 } = 0 . 599 ....
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This note was uploaded on 09/17/2009 for the course ISYE 3044 taught by Professor Alexopoulos during the Spring '08 term at Georgia Tech.

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3044hw5s09sols - 2 ISyE 3044/Spring 2009/Solutions to...

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