GATE CE 2017 Set 1 — Question 25
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Engineering Mathematics → Probability → Poisson Distribution
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Question
Vehicles arriving at an intersection from one of the approach roads follow the Poisson distribution. The mean rate of arrival is 900 vehicles per hour. If a gap is defined as the time difference between two successive vehicle arrivals (with vehicles assumed to be points), the probability (up to four decimal places) that the gap is greater than 8 seconds is ___________
Correct answer
0.1276 to 0.1372
Solution
Given:
Mean arrival rate, vehicles/hour
Convert to vehicles per second: vehicles/second.In a Poisson process, the time gaps () between successive arrivals follow an exponential distribution with the same parameter .
The probability density function of is for .
The probability that the gap is greater than is given by:
For seconds:
Rounding to four decimal places, the probability is 0.1353.
Mean arrival rate, vehicles/hour
Convert to vehicles per second: vehicles/second.In a Poisson process, the time gaps () between successive arrivals follow an exponential distribution with the same parameter .
The probability density function of is for .
The probability that the gap is greater than is given by:
For seconds:
Rounding to four decimal places, the probability is 0.1353.
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