Test 2 Solutions

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

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6 ISyE 3044/Spring 2009: Solutions to Test #2 1. (a) e - 2 . 5 =0 . 082. Using the frst 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 roundoF ±unction makes this incorrect. 2. (a) We have F ( y )= ± ( 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.±., we have Y = ± 2 U - 10 U< 1 / 2 1 - ² 2(1 - U )1 / 2 U 1 . (c) 1 - ² 2(1 - 0 . 6) = 0 . 106. (d) Triangular( - 1 , 0 , 1). 3. Sort the data values ±rom smallest to largest. The c.d.±. is
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