3044t2s09sols - 6 ISyE 3044/Spring 2009: Solutions to Test...

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Unformatted text preview: 6 ISyE 3044/Spring 2009: Solutions to Test #2 1. (a) e-2.5 = 0.082. Using the first 4 numbers, we have N1 = 3. Using the next 2 numbers, we obtain N2 = 2. 12 (b) i=1 Ui - 6 = -1.47. (c) Erlang (gamma) with shape parameter 4 and scale parameter 3. (d) a = 2, 3. (e) Poisson(25). Some wrote normal( = 24.5, = 5), but the roundoff function makes this incorrect. 2. (a) We have F (y) = (y+1)2 2 2 1 - (1-y) 2 -1 y < 0 0 y 1. Check that F (-1) = 0, F (0) = 1, and F (1) = 1. (b) Inverting the c.d.f., we have Y = (c) 1 - 2(1 - 0.6) = 0.106. (d) Triangular(-1, 0, 1). 3. Sort the data values from smallest to largest. The c.d.f. is F (t) = t3 , and the test statistic is D5 = max max i-1 i 3 3 - T(i) , max T(i) - 1i5 5 5 = max{0.643, 0.001} = 0.643. 2U - 1 0 U < 1/2 1 - 2(1 - U ) 1/2 U 1. 1i5 The adjusted test statistic is 0.11 5 + 0.12 + 5 0.643 = 1.547. Since this value is greater than the critical value c0.90 = 1.224, we reject the manager's recommendation. 4. (a) An infinite loop. (b) scale x by 2. (c) 1 w.p. 2/8; 3 w.p. 3/8; or 5 w.p. 3/8. (d) Accumulating. ...
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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 Institute of Technology.

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