Question

At a specified point on a highway, vehicles are known to arrive according to a Poisson process.
Vehicles are counted in 20-second intervals and vehicle counts are taken in 120 of these time intervals. It is noted that nocars arrive in 18 of these 120 intervals. Approximate the number of these 120 intervals in which exactly threecares arrive.

Answer 1

Step-by-step explanation:

20secsvehicles counted are taken in = 120 time intervalsno cars arrive in 18 of these 120 intervalsfrom poisson distribution P(x) = e^-λ λ^x /x!P(0) = 18/120 = e^-λλ = 0.1897 Similarly, for P(3) = e^-0.1897 X 1.897^3 /3!= 0.1707Therefore, Number of intervals in which exactly three cars arrive.= 120P(3) = 120(0.1707) = 20.47 , Approximately 21 is the number of intervals