University of California, Los AngelesEC ENGR 131ASolution to Homework1

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Homework Solution 1 Probability Instructor: Professor Roychowdhury 1. Problem 2.2 A die is tossed twice and the number of dots facing up in each toss is counted and noted in the order of occurrenc... e. (a) Find the sample space. (b) Find the set A corresponding to the event \the number of dots in first toss is not less than number of dots in second toss" (c) Find the set B corresponding to the event \number of dots in first toss is 6" (d) Does A imply B or does B imply A? (e) Find A \ Bc and describe this event in words. (f) Let C correspond to the event \number of dots in dice differs by 2". Find A\C Solution: (a) We denote the outcome of this experiment as a pair of numbers (x; y) where x is number of dots in the first toss and y is the number of dots in the second toss. Then sample space S is given by S= f(1; 1); (1; 2); (1; 3); (1; 4); (1; 5); (1; 6) (2; 1); (2; 2); (2; 3); (2; 4); (2; 5); (2; 6) (3; 1); (3; 2); (3; 3); (3; 4); (3; 5); (3; 6) (4; 1); (4; 2); (4; 3); (4; 4); (4; 5); (4; 6) (5; 1); (5; 2); (5; 3); (5; 4); (5; 5); (5; 6) (6; 1); (6; 2); (6; 3); (6; 4); (6; 5); (6; 6)g (b) A = f(1; 1); (2; 1); (2; 2); (3; 1); (3; 2); (3; 3); (4; 1); (4; 2); (4; 3); (4; 4) (5; 1); (5; 2); (5; 3); (5; 4); (5; 5); (6; 1); (6; 2); (6; 3); (6; 4); (6; 5); (6; 6)g (c) B = f(6; 1); (6; 2); (6; 3); (6; 4); (6; 5); (6; 6)g (d) We have B ⊂ A, so B implies A. (e) A \ Bc = f(1; 1); (2; 1); (2; 2); (3; 1); (3; 2); (3; 3); (4; 1); (4; 2); (4; 3); (4; 4) (5; 1); (5; 2); (5; 3); (5; 4); (5; 5)g and the event means \The first toss cannot be less than the second toss, and the first toss cannot be six." (f) A \ C = f(6; 4); (5; 3); (4; 2); (3; 1)g 2. Problem 2.8 A number U is selected uniformly at random from the unit interval. Let the events A and B be 1 [Show More]

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