You arrive at the bus stop at 10 o’clock, knowing that bus arrivals follow a Poisson distribution with a rate of two buses per hour.
i. What is the probability that you will have to wait longer than 10 minutes?
ii. If, at 10:15, the bus has not yet arrived, what is the probability that you will have to wait at least an additional 10 minutes?
If you solve this problem, you get the exact same answer (around 0.717) for both i, and ii. However, I have seen elsewhere that Poisson is not memoryless. Is that consistent with this problem? It seems to me that Poisson is memoryless based on this problem.