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midterm-soln1.pdf - Statistics 24400 Autumn 2016 Midterm...

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Statistics 24400 - Autumn 2016 Midterm Examination October 25, 2016 Name (print): 1. Please print your name in the space provided. 2. Do not sit directly next to another student. 3. Do not turn the page until told to do so. 4. This is a closed book examination, but you are permitted to have an 8x11 page of notes written on ONE side. You are permitted to have a calculator. Devices capable of communication (laptops, tablets, phones) must be powered down. 5. Please provide the answers in the space and blank pages provided. If you do not have enough space, please use the back of a nearby page, clearly indicating the identity of the continued problem. 6. Be sure to show your calculations. In order to receive full credit for a problem, you must show your work and explain your reasoning. Good work can receive substantial partial credit even if the final answer is incorrect. 7. Read through the exam before answering any questions. Our scale of credit for questions may not correlate with the level of di ffi culty you experience—use your time wisely! Question Points Score Question 1 24 Question 2 20 Question 3 30 Question 4 26 TOTAL 100 1
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1. Power Surges (24 points) Your power supply is unreliable. Power surges occur as a Poisson process with rate λ of 3 per hour. These events cause damage to your computer. You have a surge protector, but you need to remove it for 10 minutes to replace a fuse. (a) (7 pts) Assume that a single event occurring during the 10 minutes you are chang- ing the fuse will cause the system to crash. What is the probability that the system will crash? (b) (7 pts) Assume that the system will survive a single event, but two power surges during the 10 minutes used to change the fuse will cause it to crash. Now what is the probability that the system will crash? (c) (10 pts) Assume that the crash will not happen unless there are two events within 5 minutes of each other. Compute the probability that the system will crash while you change the fuse.
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