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Unformatted text preview: 1 Homework 1 key 1. A die is rolled continually until a 6 appears, at which point the experiment stops. What is the sample space of this experiment? Let E n denote the event that n rolls are necessary to complete the experiment. What points of the sample space are contained in E n ? What is ? 2. Two dice are thrown. Let E be the event that the sum of the dice is odd; let F be the event that at least one of the dice lands on 1; and let G be the event that the sum is 5. Describe the events EF, E ∪ F , FG, EF c , and EFG. EF: One lands on “1” and the other lands on an even number: {(1,2), (1,4), (1,6), (2,1), (4,1), (6,1)} E ∪ F : The sum is odd or at least one of the dice lands on “1”. FG: One die lands on “1” and the other lands on “4” {(1,4), (4,1)} EF c : Neither of the dice lands on “1”, and the sum is odd. EFG: G is already part of E. Thus EFG is FG: {(1,4), (4,1)} 3. A, B, C take turns in flipping a coin. The first one to get a head wins. The sample space of this experiment can be defined by (a) Interpret the sample space (b) Define the following events in terms of S: (i) A wins = A (ii) B wins=B (iii) (A ∪ B) c 2 4. A system is composed of 5 components, each of which is either working or failed. Consider an experiment that consists of observing the status of each component, and let the outcome of the experiment be given by the vector (x 1 , x 2 , x 3 , x 4 , x 5 ), where x i is equal to 1 if component i is working and is equal to 0 if component i is failed. (a) How many outcomes are there in the sample space of this experiment? (b) Suppose that the system will work if components 1 and 2 are both working, or if components 3 and 4 are both working, or if components 1, 3, and 5 are all working. Let W be the event that the system will work. Specify all the outcomes in W. system will work....
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 Summer '07
 Wu
 Probability

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