131A_1_hw1_solution

131A_1_hw1_solution - EE 131A Probabilities Instructor:...

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Problem Set #1: Solutions Probabilities Instructor: Vwani Roychowdhury 1. Problem 2.4 (a) S = { ( i, j ) , 1 i 6 , 1 i i } . (b) A = { (4 , j ) , 1 j 4 } . (c) A = { ( i, 3) , 3 i 6 } . (d) A = { (6 , 6) } . 2. Problem 2.7 (a) S = { (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), (3,2,1) } . (b) A 1 = { (1,2,3), (1,3,2) } , A 2 = { (1,2,3), (3,2,1) } , A 3 = { (1,2,3), (2,1,3) } . (c) A 1 A 2 A 3 = { (1,2,3) } = “all the balls are drawn in the order of their number.” (d) A 1 A 2 A 3 = { (1,2,3), (1,3,2), (2,1,3), (3,2,1) } = “at least one ball is drawn in order” (e) ( A 1 A 2 A 3 ) c = { (2,3,1), (3,1,2) } = “no ball is drawn in order” 3. Problem 2.24 P [ A ] = 1 - P ( k < = 5) = 1 - 5 X i =1 P ( k = i ) = 1 - 5 X i =1 (0 . 5 i ) = 0 . 0312 . P [ B C ] = P ( k < = 10) = 10 X i =1 P ( k = i ) = 1 - 10 X i =1 (0 . 5 i ) = 0 . 9991 . P
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This note was uploaded on 03/27/2012 for the course EE EE 131A taught by Professor Roychowdhary during the Spring '05 term at UCLA.

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131A_1_hw1_solution - EE 131A Probabilities Instructor:...

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