# Physics307L:People/Giannini/Poisson

Steve Koch 20:07, 21 December 2010 (EST): Good job with this lab, very nice plots and data. Partner: Richard T. Meyers

For my data analysis look here.

## Contents

## Purpose

- To become familiar with the Poisson Distribution
- To procure Poisson Distributed data and analyze it for mean, error, variance and Chi-Squared values and explain the numbers obtained.

## Summary

The lab is set up as a photon multiplier tube attached to an amplifier which is driven by a computer. The software on the computer determines how the amplifier functions (pre-amp, amp in etc.) and collects data once it begins to run. This data is a point, at a value that corresponds to the number of events recorded, for each time interval you choose (20ms, 40ms etc) with a total of 2046 points. These data plots are what I used to help me determine whether I should use pre-amp or amp-in. For more on the histograms of these data points look here. We then used these histograms to overlay a Poisson distribution. We also determined the standard deviation of each of our histograms as well as their mean.

## Comparison to Poisson Distribution

Overall, the graphs for 10ms, 20ms, 40ms, 80ms, and 100ms overlap with the Poisson Distribution I have overlay-ed on them, although they do not do so perfectly, but do so to an extent that you can say that my data is most likely Poisson Distributed. Also, as the time interval gets better, the data becomes even more Poisson Distributed, as represented by the decreasing deviation from a normal Poisson Distribution.

## Chi-Squared

This has given me the most problems, since I am rather uncertain about what gold is talking about in his analysis section. Since my number of degrees of freedom are equivalent the number of bins I have, and that each bin only represents the number of times the same number has occurred. Also, since the mean of each is the number that the bin is representing, I can only assume that Gold wished to have the chi-square value for the histogram as a whole, with a calculated standard deviation for all of my data points. I will proceed in this manner.

The equation I am using is can be found here on the third sheet.

I'll be using 10ms,20ms, 40ms, 80ms, and 100ms for this part, since I have found that my data with smaller time intervals is more poisson-like in its distribution than those with larger time intervals.

10ms: **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 0.3599087}**
20ms: **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 1.5856168}**
40ms: **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 4.6672262}**
80ms: **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 0.0747959}**
100ms: **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 24.684542}**

## What Did I Learn?

That the more trials you take, the easier it is to interpret your data.

## What Did I Explore Outside of the Lab procedure?

We took extra trials and also tested 'pre-amp' to see if it was Poisson Distributed.

## What Would make the Lab Better Next Year?

Going over the last part of this lab was rather difficult and I ended up having to make assumptions. It would be nice if we had covered chi-squared in depth by now.