Consider the radar detection system at all airports. The tree diagram in Figure EL.2.5 depicts the statistical performance of the system, including the prior probabilities. Let A denote the event that an aircraft is in the sky, and D denote the event that an aircraft is detected. Determine the probability that an aircraft is not in the sky. (b) What is the probability that an aircraft is detected while there is an aircraft in the sky? What is the probability that no aircraft is detected while there is no aircraft in the sky? Determine the probability of false alarm. Determine the probability of missed detection.
P(A | D) = P(D | A) * P(A) / P(D)
P(A | D') = P(D' | A') * P(A') / P(D')
P(D) = P(D | A) * P(A) + P(D | A') * P(A')
P(D') = P(D' | A) * P(A) + P(D' | A') * P(A')
Figure EL.2.5: P(A) = 0.92, P(D | A) = 0.985, P(D | A') = 0.975
