4. You point your Geiger counter at a banana, waiting for it to click. You know that the time you have to wait is exponentially distributed with rate >= Unfortunately, 10% of all Geiger counters have been sabotaged by Big Banana. A sabotaged Geiger counter, when pointed at a banana, will instead click after every 60 seconds to lull you into complacency. (a) Determine the CDF of the waiting time until your Geiger counter clicks (you do not know if your Geiger counter has been sabotaged). (b) If you have been waiting for 30 seconds and your Geiger counter still hasn't clicked yet, what is the probability that it has been sabotaged?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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4. You point your Geiger counter at a banana, waiting for it to click. You know that the time
you have to wait is exponentially distributed with rate >= 1
Unfortunately, 10% of all Geiger counters have been sabotaged by Big Banana. A sabotaged
Geiger counter, when pointed at a banana, will instead click after every 60 seconds to lull
you into complacency.
(a) Determine the CDF of the waiting time until your Geiger counter clicks (you do not
know if your Geiger counter has been sabotaged).
(b) If you have been waiting for 30 seconds and your Geiger counter still hasn't clicked yet,
what is the probability that it has been sabotaged?
Transcribed Image Text:4. You point your Geiger counter at a banana, waiting for it to click. You know that the time you have to wait is exponentially distributed with rate >= 1 Unfortunately, 10% of all Geiger counters have been sabotaged by Big Banana. A sabotaged Geiger counter, when pointed at a banana, will instead click after every 60 seconds to lull you into complacency. (a) Determine the CDF of the waiting time until your Geiger counter clicks (you do not know if your Geiger counter has been sabotaged). (b) If you have been waiting for 30 seconds and your Geiger counter still hasn't clicked yet, what is the probability that it has been sabotaged?
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