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CEE 3040
Fall 2009
CEE 304 – Section 5
Review of Poisson Processes
A Poisson process satisfies three conditions:
1.
The probability of an arrival in a short interval
∆
t equals
λ∆
t.
For small
∆
t, the probability of 2 arrivals within
∆
t can be neglected.
Here
λ
is the arrival rate with units per time, or counts per time.
2.
The arrival rate
λ
is constant.
3.
The number of arrivals in nonoverlapping intervals are independent.
Examples of Poisson Processes:
1.
An engineer has instrumented several towers to measure wind gust speed and other
parameters. Events of magnitude of interest occur on average once every 3 months.
Assume the arrival of such events are a Poisson process, and the experiment lasts 18
months.
a.)
What is the mean and variance of the number of events that will occur?
Solution:
Mean = Var = 6
b.)
What is the probability she sees 4 or fewer events during the 18 mo. experiment?
Solution:
Use Poisson tables: P[X ≤ 4  ν = 6] = 0.285
c.)
If she decided to run the experiment until 5 events are observed, what is the mean and
variance of the length of the resulting experiment?
Solution:
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This note was uploaded on 10/13/2010 for the course CEE 3040 at Cornell University (Engineering School).
 '08
 Stedinger

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