Q. An observer counts vehicles per hour at a specific location on a highway. Assuming that the arrival of vehicles at the location follows a Poisson distribution, the probability that more than two vehicles arrive over a time interval is

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Solution:

The average arrival rate, is or vehicles per second.
According to poisson distribution,

Where, probability of having vehicles arrive in time .
Average vehicle flow or arrival rate in per unit time
duration of the time interval over which vehicles are counted
base of natural logarithm



For more than two vehicles,