. Find the probability that 5 patients present in the first hour b. What is the probability that the time between arrivals of the 4th and 5th patients is more than 1/2 hour? c. What is the probability that the arrival time of the second patient is more than 1 hour?

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The arrival of patients in a hospital follows the Poisson process at a rate of 8 people/hour.
a. Find the probability that 5 patients present in the first hour
b. What is the probability that the time between arrivals of the 4th and 5th patients is more than 1/2 hour?
c. What is the probability that the arrival time of the second patient is more than 1 hour?
What is the mean and variance of time until the arrival of the 8th patient?

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