4. (12 pts) A professor uses a presentation pointer that works with 2 batteries. If any battery in use fails, then the p

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4 12 Pts A Professor Uses A Presentation Pointer That Works With 2 Batteries If Any Battery In Use Fails Then The P 1 (177.06 KiB) Viewed 93 times

4. (12 pts) A professor uses a presentation pointer that works with 2 batteries. If any battery in use fails, then the pointer does not work. Assume that the lifetime of a battery is exponentially distributed with a mean of 30 days. (a) (4 pts) Explain how to set this up as a renewal process {N(t): t >0}. In particular, state what N(t) stands for and describe the interevent distribution. (b) [4 pts] As soon as a battery in use fails, the professor immediately replaces it with a new battery. At what rate does she have to change batteries? (c) (4 pts. Now suppose that she does not keep any surplus batteries on hand. Every time a battery in use fails, she orders a new battery online. Assume that the amount of time it takes for her to get the new battery has a uniform distribution between 1 and 7 days. What is the average rate that she changes batteries?