Question

Consider the assumptions of a Poisson process given in class. Suppose the arrival of cars to a restaurant follows a Poisson process. Which of the following examples do not violate an assumption of the Poisson process?

		two cars arrive at a restaurant at exactly the same time
		the probability of one car arriving between 9:10 and 9:20 is the same as the probability of one car arriving between 9:25 and 9:35
		the probability of one car arriving between 9:04 and 9:06 depends on whether there was an arrival between 9:03 and 9:04
		the probability of one car arriving between 9:05 and 9:15 is the same as the probability of one car arriving between 9:00 and 9:05

Answer 1

the probability of one car arriving between 9:10 and 9:20 is the same as the probability of one car arriving between 9:25 and 9:35

the probability of one car arriving between 9:05 and 9:15 is the same as the probability of one car arriving between 9:00 and 9:05

These above 2 examples does not violate the assumption of poisson process.Because

• The rate at which events occur is constant. The rate cannot be higher in some intervals and lower in other intervals.