l. A security camera is used to monitor a particular surveillance area to report
ID: 3172802 • Letter: L
Question
l. A security camera is used to monitor a particular surveillance area to report whether there is any threat present or not. The probability that the camera correctly detects an actual threat as "threat found" is 0.8. The probability that the camera correctly reports no threat as "no threat found" is 0.9. Suppose the probability of an actual threat being present in the surveillance area is 0.6. a. What is the probability that the camera reports "threat found"? (4 Marks) b. Given that the camera reports "threat found", what is the probability that there are actual threats in the surveillance area? (3 Marks) Answer parts c) and d) by assuming that an actual threat is always present (i.e., probability of threat presence is 1) c. What is the probability that the camera reports "threat found"? (1 Mark) d. An identical second camera is used to increase the accuracy of threat reporting capability. The cameras are operating independently and monitoring the same surveillance area. Find the probability that the combined system reports the threat accurately (at least one camera should report "threat found'). (2 Marks OR 2. Continuous Random variables a. Assume a random variable X is normally distributed with a mean of 10 and a variance of 16. Find A such that POK A) 0.7. (4 marks) Now consider the probability function g(x) kr 0Explanation / Answer
1) P(camera reports "threat found") = 0.6x0.8+0.4x0.1 =0.52
2) P(actual threat | camera reports "threat found")
= P(actual threat and camera reports "threat found")/ P(camera reports "threat found") = 0.6x0.8/0.52 = 0.923
C) P(camera reports "threat found") = 0.8
D) P(at least one camera reporting threat) = 1-P(both camera not reporting threat)
= 1 - (0.2x0.2)
= 0.96
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