The number of people who enter an elevator on the ground floor is a Poisson random variable with mean 10. If there are N floors above the ground floor and if each person is equally likely to get off at any one of these N floors, independently of where the others get off, compute the expected number of stops that the elevator will make before discharging all of its passengers.

Given Information:

Distribution = Poisson

Mean = 10

Required Information:

Expected number of stops = ?

Explanation:

The number of people entering on the elevator is a Poisson random variable.

There are N floors and we want to find out the expected number of stops that the elevator will make before discharging all of its passengers.

Mean = μ = 10

The expected number of stops is given by

Where m is the decay rate and is given by

Decay rate = m = 1 /μ = 1/10 = 0.10

Therefore, the expected number of stops is

If we know the number of floor (N) then we can the corresponding expected value.

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068