GATE CE 2019 Set 1 — Question 56
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Engineering Mathematics → Probability → Microscopic Parameters
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Question
Traffic on a highway is moving at a rate of vehicles per hour at a location. If the number of vehicles arriving on this highway follows Poisson distribution, the probability (round off to 2 decimal places) that the headway between successive vehicles lies between and seconds is ________
Correct answer
0.17 to 0.19
Solution
Given:
Arrival rate, vehicles/hour vehicles/second.For a Poisson arrival process, the time headway between successive vehicles follows an exponential distribution with the same parameter .
The probability density function of headway is for .The probability that the headway lies between and seconds is:Substituting :Rounding off to decimal places, the probability is .
Arrival rate, vehicles/hour vehicles/second.For a Poisson arrival process, the time headway between successive vehicles follows an exponential distribution with the same parameter .
The probability density function of headway is for .The probability that the headway lies between and seconds is:Substituting :Rounding off to decimal places, the probability is .
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