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 no cars arrive in 18 of these 120 intervals. Approximate the number of these 120 intervals in which exactly three cars arrive.

Answer 1

Answer:

Explanation:

• Given vehicles are counted = 20secs

• vehicles counted are taken in = 120 time intervals

• no cars arrive in 18 of these 120 intervals

• from poisson distribution P(x) = e^-λ λ^x /x!

• P(0) = 18/120 = e^-λ

• λ = 0.1897

Similarly, for P(3) = e^-0.1897 X 1.897^3 /3!

= 0.1707

• Therefore, Number of intervals in which exactly three cars arrive.

• = 120P(3) = 120(0.1707)

• = 20.47 , Approximately 21 is the number of intervals