08SimHw2sol_all

08SimHw2sol_all - IEOR 4404 Assignment #2 Solutions...

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Unformatted text preview: IEOR 4404 Assignment #2 Solutions Simulation 3rd October 2008 Prof. Mariana Olvera-Cravioto Page 1 of ?? Assignment #2 Solutions 1. (a) p X ( x ) = ∑ 3 y =0 p ( x,y ) for x = 0,1,2 and 0 otherwise. Thus, p X (0) = 6 30 , p X (1) = 10 30 and p X (2) = 14 30 . p Y ( y ) = ∑ 2 x =0 p ( x,y ) for y = 0,1,2,3 and 0 otherwise. Thus, p Y (0) = 3 30 , p Y (1) = 6 30 , p Y (2) = 9 30 and p Y (3) = 12 30 . The plot for p X ( x ) versus x consists of the three points: (0, 6 30 ), (1, 10 30 ) and (2, 14 30 ). Similarly, the plot for p Y ( y ) versus y consists of the four points: (0, 3 30 ), (1, 6 30 ), (2, 9 30 ) and (3, 12 30 ). (b) X and Y are not independent. To see why, simply note that p (0 , 0) 6 = p X (0) × p Y (0). (c) F X ( x ) = , x < 6 30 , ≤ x < 1 16 30 , 1 ≤ x < 2 1 , x ≥ 2 F Y ( y ) = , y < 3 30 , ≤ y < 1 9 30 , 1 ≤ y < 2 18 30 , 2 ≤ y < 3 1 , x ≥ 3 See Figure 1 and 2 on the last page for the plots. (d) E [ X ] = ∑ x xP X ( x ) = 38 / 30 E [ X 2 ] = ∑ x x 2 P X ( x ) = 66 / 30 Thus, var [ X ] = E [ X 2 ] = E [ X ] 2 = 536 / 900 Similarly,...
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This note was uploaded on 11/17/2010 for the course IEOR 4404 taught by Professor C during the Spring '10 term at Columbia.

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08SimHw2sol_all - IEOR 4404 Assignment #2 Solutions...

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