Assume that in a traffic junction, the cycle of the traffic signal lights is 2 minutes of green (vehicle does not stop) and 3 minutes of red (vehicle stops). Consider that the arrival time of vehicles at the junction is uniformly distributed over 5 minute cycle. The expected waiting time (in minutes) for the vehicle at the junction is ___________ .
Correct Answer
0.9-0.9
Solution & Step-by-step Explanation
Let X be the time at which vehicle arrives the traffic junction
Let Y be the waiting time
If vehicle arrives between X = 0 and X = 2, the waiting time will be zero.
If vehicle arrives at X ≥ 2, the waiting time will be (5 - X).
Y = ≤ft\{ {*20c 0,&X < 2\\ 5 - X,&X ≥ 2 } .
Expected waiting time,
= 0.9
Let Y be the waiting time
If vehicle arrives between X = 0 and X = 2, the waiting time will be zero.
If vehicle arrives at X ≥ 2, the waiting time will be (5 - X).
Y = ≤ft\{ {*20c 0,&X < 2\\ 5 - X,&X ≥ 2 } .
Expected waiting time,
= 0.9