midterm-soln1.pdf

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

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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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