Section_5 - CEE 304 Section 5 Review of Poisson Processes A...

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CEE 304 – Section 5 (9-27-06) Review of Poisson Processes A Poisson process satisfies three conditions: 1. The probability of an arrival in a short interval Δ t equals λΔ t. For small Δ t, the probability of 2 arrivals within Δ 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 non-overlapping 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? Number of arrivals in 18months is Poisson ( 6 18 3 1 = = = t λ ν ) E(X) = Var(X) = ν = 6 b.) What is the probability she sees 4 or fewer events during the 18 mo. experiment? Use Poisson tables, ( ) 285 . 0 6 | 4 = = ν X P 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?
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