Question

Suppose a shop opens at 9 am. During the release of a long-awaited product, people start arriving at the shop at 8 am and queue in front of the shop. The arrivals follow a non-homogeneous Poisson process with a rate function λ(t) = 25t² (t = 0 refers to 8 am). What is the rate of arrivals at 9 am?

1) 625
2) 900
3) 1225
4) 2025

Answer 1

The rate of arrivals at 9 am is 25.

Step-by-step explanation:

The rate of arrivals at 9 am can be found by evaluating the rate function, λ(t), at t = 1 (because 9 am corresponds to t = 1 in this scenario). Plugging in the value of t, we have λ(1) = 25(1)^2 = 25. Therefore, the rate of arrivals at 9 am is 25.