GE 331-Lecture 7 peroblems

GE 331-Lecture 7 peroblems - Q1. The MIT soccer team has 2...

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Q1. The MIT soccer team has 2 games scheduled for the weekend. P(not losing first game) = 0.4 P(not losing second game) = 0.7 Results of the games are independent of each other. If it does not lose a game, it is equally to win or tie. The team receives 2 points for a win, 1 for a tie and 0 for a loss. Find the PMF of the number of points the team wins over the weekend. Solution: :number of point the team earn on the weekend : points received from game i, i=1,2 i i X Y The sample space:     0,1,2,3,4 , 0,1,2 XY  Since                 1 1 1 2 2 2 P not losing first game 0.4 P not losing second game 0.7 And if it does not lose a game, it is equally to win or tie,then we know: P 0 0.6,P 1 0.2,P 2 0.2 P 0 0.3,P 1 0.35,P 2 0.35 Y Y Y Y Y Y Thus                           12 1 2 1 2 1 2 1 2 1 2 1 2 1 2 0 0 0 0.6 0.3 0.18 1 0 1 1 0 0.6 0.35 0.2 0.3 0.27 2 0 2 1 1 2 0 0.6 0.35 0.2 0.35 0.2 0.3 0.34 3 1 2 2 1 0.2 0.35 0.2 0.35 0.14 4
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GE 331-Lecture 7 peroblems - Q1. The MIT soccer team has 2...

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