# Physics307L F07: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 :

${\displaystyle f(k;\lambda )={\frac {\lambda ^{k}e^{-\lambda }}{k!}},\,\!}$

Where ${\displaystyle \lambda }$ is the amount of successes in a given period and ${\displaystyle k}$ is the amount of ocurances.

Data

40ms Dwell Time

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)
00:17, 10 December 2007 (CST)
You guys took some nice data, but it's not clear that you learned much from the analysis? e.g., what is "chi-squared" representing?
Dwell Time ${\displaystyle chi^{2}}$ Average ${\displaystyle \lambda }$
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.