IE230Spring 2021 Prac Prob for 01 PDF

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Practice problems for IE 230. Problem set 1...

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IE230 – Spring 2021

Practice Problems for Quiz on Monday (01/25/2021)

[Q1] In an experiment, a six-sided die is rolled continually until a 6 appears, at which point the experiment stops. What is the sample space of this experiment? [Q2] 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, x2, x3, x 4, x5), where xi 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? (Note: you do NOT need to write out the complete sample space, just provide the number of outcomes in the sample space. However, you NEED to provide the details as how you obtain the number.) (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 . (Note: here you DO need to write out all the elements in the event W , not just a number.) (c) Let A be the event that components 4 and 5 are both failed. Write out all the outcomes in the event A ∩ W . [Q3] Three events are shown on the Venn diagram in the following figure: A

B

C

Reproduce the figure and shade the region that corresponds to each of the following events. (a) A¿ (b) 1 A ¨ B2 ´ 1 A ¨ B¿ 2 (c) 1A ¨ B2 ´ C (d) 1B ´ C2¿ (e) 1A ¨ B2¿ ´ C 1...