prof benhabib s office has surveillance system with one motion detector only the detector is pro

(a) First, we need to consider the systematic error of -0.1 volt. This means that the actual sig

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Prof. Benhabib's Office has a surveillance system with only one motion detector. The detector is programmed to send a 5-volt signal to the controller when it detects motion, which in turn notifies the campus police. The controller will assume unauthorized presence ONLY if it receives a signal that is more than 4.5 volts. The motion detector's output signal of 5 volts is subjected to a systematic (calibration) error of -0.1 volt, as well as random noise that has a normal distribution with the following (population) statistics: noise = 0.0 and Ïƒnoise = 0.4 volt. (a) Calculate the probability that a break-in into Prof. Benhabib's Office to remove valuable documents (for example, MIE23 exams) will NOT be detected. [15 points] (b) In order to increase the certainty of detection of a break-in to at least 99%, Prof. Benhabib would like to increase the number of motion detectors connected to the controller. The controller will assume unauthorized presence ONLY if it receives a signal that is more than 4.5 volts from at least one (1) detector. Based on the given detector characteristics and your answer to Part (a) above, calculate the minimum number of detectors, nmin, which need to be installed. [Hint: You may use the Binomial Probability Function]: [5 points]

          Prof. Benhabib's Office has a surveillance system with only one motion detector. The detector is programmed to send a 5-volt signal to the controller when it detects motion, which in turn notifies the campus police. The controller will assume unauthorized presence ONLY if it receives a signal that is more than 4.5 volts. The motion detector's output signal of 5 volts is subjected to a systematic (calibration) error of -0.1 volt, as well as random noise that has a normal distribution with the following (population) statistics: noise = 0.0 and Ïƒnoise = 0.4 volt.

(a) Calculate the probability that a break-in into Prof. Benhabib's Office to remove valuable documents (for example, MIE23 exams) will NOT be detected. [15 points]

(b) In order to increase the certainty of detection of a break-in to at least 99%, Prof. Benhabib would like to increase the number of motion detectors connected to the controller. The controller will assume unauthorized presence ONLY if it receives a signal that is more than 4.5 volts from at least one (1) detector. Based on the given detector characteristics and your answer to Part (a) above, calculate the minimum number of detectors, nmin, which need to be installed. [Hint: You may use the Binomial Probability Function]: [5 points]

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