Discrete & Continuous Random Variables - Statistics

Example: Engine Shutdown (continued)Given that both engines are shut down during a given flight (rare), what is thechance that both events happen within half an hour of takeoff or landing?Assuming independence of the shutdown times X 1 and X 2P(max(X 1 ,X 2 ) ≤ 0.5 ∪ min(X 1 ,X 2 ) ≥ 7.5)= P(max(X 1 ,X 2 ) ≤ 0.5) + P(min(X 1 ,X 2 ) ≥ 7.5)= P(X 1 ≤ 0.5) · P(X 1 ≤ 0.5) + P(X 1 ≥ 7.5) · P(X 2 ≥ 7.5)= 1 16 · 116 + 116 · 116 = 0.0078125On a 737 an engine shutdown occurs about 3 times in 1000 flight hours.The chance of a shutdown in an 8 hour flight is 8 · 3/1000 = 0.024,the chance of two shutdowns is 0.024 2 = 0.000576, the chance of two shutdownswithin half an hour of takeoff of landing is 0.000576 · 0.0078125 = 4.5 · 10 −6 .50