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econ310_f09_ps6_ans - Econ 310 Problem Set#6 Solutions...

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Econ 310: Problem Set #6 Solutions Andres Aradillas-Lopez 1. Exercise 4.52. (a) Curve on the below. A good procedure is to draw the curve flrst, locate the points where the curvature changes, then mark the hori- zontal axis. Students may at flrst make mistakes like drawing a half- circle instead of the correct "bell-shaped" curve or being careless about locating the standard deviation. (b) About 0.017: P ( Y > 300) = P Y ¡ 266 16 > 300 ¡ 266 16 = P ( Z > 2 : 125). Software gives 0.0168; Table A gives 0.0166 for ¡ 2 : 13 and 0.0170 for ¡ 2 : 12 (so the average is again 0.0168). 2. Exercise 4.60. Let "S" mean that a student supports funding and "O" mean that the student opposes funding. (a) P ( SSO ) = (0 : 6)(0 : 6)(0 : 4) = 0 : 144. (b) See the top two lines of the table below. (c) The distribution is given in the bottom two lines of the table. For example, P ( X = 0) = (0 : 6)(0 : 6)(0 : 6) = 0 : 216, and in the same way, P ( X = 3) = 0 : 4 3 = 0 : 064. For P ( X = 1), note that each of the three arrangements that give X = 1 have probability 0.0144, so P ( X = 1) = 3(0 : 144) = 0 : 432.
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