1. Busy people arrive at the park according to a Poisson process with rate λ1=3/hour and stay in the park for exactly 1/6 of an hour. Relaxed people arrive at the park according to a Poisson process with rate λ2=2/hour and stay in the park for exactly half an hour. The arrivals of busy and relaxed people are independent processes. Assume that no other people arrive at the park. Is the process of total arrivals at the park a Poisson process? If yes, enter the rate of that process in the answer box below. If it is not, enter 0.

Question

2. Whenever a relaxed person exits the park, he/she enters a nearby coffee shop. (Assume, for simplicity, that going from the park to the coffee shop takes zero time.) Is the process of arrivals of relaxed persons at the coffee shop a Poisson process? If yes, enter the rate of that process in the answer box below. If it is not, enter 0.

Answer 1

a) 5
b) 2

Answer 2

a/ e^(-3)
b/ 3/2*e^(-3/2)

Answer 3

use this. surely this is correct

a) e^(-0.5)
b) 3/2*e^(-3/2)

Answer 4

For part 2.
Rate of total arrival is 5
Rate of relaxed persons to coffee shop is 2

Answer 5

1.
a) e^(-0.5)
b) 3/2*e^(-3/2)

2.
5
2