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3044t2s09sols

# 3044t2s09sols - 6 ISyE 3044/Spring 2009 Solutions to Test#2...

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6 ISyE 3044/Spring 2009: Solutions to Test #2 1. (a) e - 2 . 5 = 0 . 082. Using the first 4 numbers, we have N 1 = 3. Using the next 2 numbers, we obtain N 2 = 2. (b) 12 i =1 U i 6 = 1 . 47. (c) Erlang (gamma) with shape parameter 4 and scale parameter 3. (d) a = 2 , 3. (e) Poisson(25). Some wrote normal( μ = 24 . 5 , σ = 5), but the roundoff function makes this incorrect. 2. (a) We have F ( y ) = braceleftBigg ( y +1) 2 2 1 y < 0 1 (1 - y ) 2 2 0 y 1 . Check that F ( 1) = 0, F (0) = 1, and F (1) = 1. (b) Inverting the c.d.f., we have Y = braceleftBigg 2 U 1 0 U < 1 / 2 1 radicalbig 2(1 U ) 1 / 2 U 1 . (c) 1 radicalbig 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 ) = t 3 , and the test statistic is
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