Question

Poisson. Process non homogeneous

I need some one to explain how to get (8-t)/2 and why delta is (1 to 7) . Also, please show the hidden steps of integral from 1 to 7 lambda (s)ds as the notes skip the computation

EXAMPLE 1. Customers arrive at a service facility according to a non-homogeneous Poisson process with a rate of 3 customers/hour in the period between 9am and 11am. After llam, the rate is decreasing linearly from 3 at 11am to zero at 5pm. Find the probability that there will be not more than 15 customers between 10am and 4pm. Taking 9am as an initial time, we have 2(t) = 3 for t € (0,2), and (t) = (8 - 1)/2 for te (2,8). For the interval A = [1,7], the expected number of customers Xa= 11.75, and we get (for example, using Excel) that P(NA < 15) = PoissonDist(15;11.75) = 0.862. O ſ, a(s)ds = In the general case, when the rate can change in time, the number of arrivals may be small during a long period, and may be large during a short period.

Answer 1