Physics307L F09:People/Trujillo/Poisson
POISSON
Definition
The Poisson Distribution is a discrete distribution which takes on the values X = 0, 1, 2, 3, ... . It is often used as a model for the number of events (such as the number of telephone calls at a business or the number of accidents at an intersection) in a specific time period. It is also useful in ecological studies, e.g., to model the number of prairie dogs found in a square mile of prairie.
The Poisson distribution is determined by one parameter, lambda. The distribution function for the Poisson distribution is :
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle f(k;\lambda)=\frac{\lambda^k e^{-\lambda}}{k!},\,\!}
Where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \lambda} is the amount of successes in a given period and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle k} is the amount of ocurances.
Data
We took data using a Multichannel Analyzer (MCA)which detects the amount of events occurring in a particular time period. Each channel represents the number of bins in time. The RAW data is found here
^{SJK 00:17, 10 December 2007 (CST)}Dwell Time | Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle chi^2} | Average Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \lambda} |
---|---|---|
80ms | .45714 | 0.70703 |
100ms | .4683 | 0.62891 |
200ms | .9374 | 1.2070 |
400ms | 2.585 | 2.7617 |
800ms | 5.745 | 6.0234 |
1s | 7.7272 | 7.3242 |
10s | 73.902 | 73.366 |
Summary
Well, at first i was thinking that this experiment was going to be easy but it turns out that the majority of the lab is not taking the data but analyzing the data. I originally thought that I would have time to cook up snazzy LabVIEW program that would display all the distributions it an animated mode and a "single shot" mode but. I got some insight from Tomas on house exactly this is supposed to work being that he went above and beyond on the analysis.