GATE CE 2014 Set 2 — Question 37
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Engineering Mathematics → Probability → Poisson Distribution
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Question
An observer counts veh/h at a specific highway location. Assume that the vehicle arrival at the location is Poisson distributed, the probability of having one vehicle arriving over a -second time interval is ____________
Correct answer
0.25 to 0.28
Solution
Step 1: Identify the arrival rate and time interval.
Arrival rate, vehicles/hour.
Time interval, seconds.Step 2: Convert the time interval to the same units as the arrival rate (hours).
hours.Step 3: Calculate the mean number of arrivals () in the -second interval.
vehicles.Step 4: Use the Poisson distribution formula to find the probability of exactly one arrival ().
The Poisson probability mass function is .
.Step 5: Calculate the numerical value.
Using :
.The probability of exactly one vehicle arriving in a -second interval is approximately .
Arrival rate, vehicles/hour.
Time interval, seconds.Step 2: Convert the time interval to the same units as the arrival rate (hours).
hours.Step 3: Calculate the mean number of arrivals () in the -second interval.
vehicles.Step 4: Use the Poisson distribution formula to find the probability of exactly one arrival ().
The Poisson probability mass function is .
.Step 5: Calculate the numerical value.
Using :
.The probability of exactly one vehicle arriving in a -second interval is approximately .
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