AMS 311 (Fall, 2011) Joe Mitchell PROBABILITY THEORY Homework Set # 1 Due at the beginning of class on Thursday, September 8, 2011. Reminder: Show your reasoning! Read: Ross, sections 1.1-1.4 of Chapter 1, and sections 2.1-2.5 of Chapter 2 . SPECIFICS OF READING ASSIGNMENT: Examples to read carefully: Chapter 1: 2a–2e; 3a–3f; 4a–4e Chapter 2: 3a, 3b, 4a, 5a–5j, 5l (1). (13 points) A system is comprised 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 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 working, or if components 1, 3, and 5 are all working. Let W be the event that the system will work. Specify all of the
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This note was uploaded on 09/21/2011 for the course AMS 311 taught by Professor Tucker,a during the Fall '08 term at SUNY Stony Brook.