User:Tyler Wynkoop/Tyler's Page/Poisson: Difference between revisions
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The Poisson Distribution is a way to describe, via probability, the likelihood of random events. The events can be nearly any randomly occurring phenomena that are independent of all other events in the set. For example: rain drops hitting a predefined area or the decay rate of a subatomic particle. In our set up, we measured the number of muons collected by a detector over a certain period of time. The longer the total amount of time, the more likely that a pattern emerges. With continuous, random, and independent events, the pattern yields a Poisson Distribution. Here, the likelihood of a random Poisson event over a certain period of time is: | The Poisson Distribution is a way to describe, via probability, the likelihood of random events. The events can be nearly any randomly occurring phenomena that are independent of all other events in the set. For example: rain drops hitting a predefined area or the decay rate of a subatomic particle. In our set up, we measured the number of muons collected by a detector over a certain period of time. The longer the total amount of time, the more likely that a pattern emerges. With continuous, random, and independent events, the pattern yields a Poisson Distribution. Here, the likelihood of a random Poisson event over a certain period of time is: | ||
<math>P(k,\lambda) = \frac{e^{-\lambda} (\lambda)^k}{k!}</math> | <math>P(k,\lambda) = \frac{e^{-\lambda} (\lambda)^k}{k!}</math> | ||
where λ is the expected value, and k is the number of events. | |||
'''Set Up''' | |||
In this lab, there really was very little set up. A muon detector with some simple analyzing software are all that are required. We used periods of 1ms, 2ms, 4ms, 8ms, .1s, .2s, .4s, .8s, and 1s taking 2047 data points for each time interval. | |||
Latest revision as of 16:22, 14 December 2010
Poisson Distribution
Theory
The Poisson Distribution is a way to describe, via probability, the likelihood of random events. The events can be nearly any randomly occurring phenomena that are independent of all other events in the set. For example: rain drops hitting a predefined area or the decay rate of a subatomic particle. In our set up, we measured the number of muons collected by a detector over a certain period of time. The longer the total amount of time, the more likely that a pattern emerges. With continuous, random, and independent events, the pattern yields a Poisson Distribution. Here, the likelihood of a random Poisson event over a certain period of time is:
[math]\displaystyle{ P(k,\lambda) = \frac{e^{-\lambda} (\lambda)^k}{k!} }[/math]
where λ is the expected value, and k is the number of events.
Set Up
In this lab, there really was very little set up. A muon detector with some simple analyzing software are all that are required. We used periods of 1ms, 2ms, 4ms, 8ms, .1s, .2s, .4s, .8s, and 1s taking 2047 data points for each time interval.
