quiz1_2005_soln

quiz1_2005_soln - Quiz #1 Solutions Problem 1 Define the...

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Quiz #1 Solutions Problem 1 Define the following events: D: dangerous conditions D c : normal conditions T: alarms indicated dangerous conditions T c : alarm indicates normal conditions Given: P[T |D] = 95 0 . P[T c | D] = 05 0 . P[T | D c ] = 005 0 . P[T c | D c ] = 995 0 . P[D] = 005 0 . P[D c ] = 995 0 . (a) Probability of false alarm: P[D c | T] = P[D c ]. P[T |D c ] P[T] P[T] is found using the Total Probability Theorem as P[T] = P[T | P ]. D [D] P + [T | D c P ]. [D c ] Therefore, P[D c | T] = P[D c ]. P[T |D c ] = 0.5116 P[T] (b) Probability of unidentified critical condition: P[D | T c ] = P[ ]. D P[T c | D] = 0.0002525 P[T c ] (c) Number of False Alarms = P[D c | T] × P[T] × 365 × 10 = 18 times
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Number of unidentified dangerous conditions= P[D | T c ] × P[T c ] × 365 × 10 = 1 time The alarm system therefore gives 18 false alarms in the 10 year period , which can be a hassle. It does however fail to identify only one dangerous condition, so performs well here. Good alarms aim to minimize false alarms and eliminate unidentified conditions. Problem 2 (a) The answer to this question is somewhat subjective, and so will be different depending on who answers, but here are a few ideas that should be included. The three conditions that a point process need to satisfy to be Poisson are:
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quiz1_2005_soln - Quiz #1 Solutions Problem 1 Define the...

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