User:Nathan Giannini/Notebook/Physics 307L/101018: Difference between revisions

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The differences become more like those of a poisson distribution as the time interval decreases. This leads me to suspect that if we used an even smaller interval we would achieve an even greater similarity to a normal poisson distribution. I also notice that for the 100ms, 400ms, and 800ms the poisson distribution becomes like a gaussian, and is most likely no longer poisson distributed, but normally distributed.
The differences become more like those of a poisson distribution as the time interval decreases. This leads me to suspect that if we used an even smaller interval we would achieve an even greater similarity to a normal poisson distribution. I also notice that for the 100ms, 400ms, and 800ms the poisson distribution becomes like a gaussian, and is most likely no longer poisson distributed, but normally distributed.
{{SJK Comment|l=20:06, 21 December 2010 (EST)|c=Actually, all of your data look like Poisson!  Poisson is approximately normal, as the expected number gets higher.}}


=Thanks=
=Thanks=

Latest revision as of 18:06, 21 December 2010

My partner is Richard T. Meyers

Safety

  • Beware of Electric Shock
  • Do Not mess with PMT

Procedure

The Procedure can be found here and the analysis can be found here

My Experience in the Lab

This is a simple lab that required me to start a program and then let it run to completion. We saved each of our our trials, for varying time intervals, and then uploaded them to Google Docs. All of the analysis can be easily done by creating histograms for each trial we took and then creating a chart that contains a Poisson Distribution Overlay. We also became aware of a differing use for our amp. The two choices were "Pre-Amp" and "Amp-In". We took trials with both so that we could determine which one was Poisson Distributed.

Data

SJK 19:51, 21 December 2010 (EST)

19:51, 21 December 2010 (EST)
Very nice plots. I think you have an error in your 200 ms overlay.

The Red Line is the Poisson Distribution. The charts can be viewed by clicking either 'Chart 1' or 'Chart 2'. {{#widget:Google Spreadsheet |key=0AlAK7TMhL37adHhRUi1CUmw3UVJMQlduajRweGVYSnc |width=1000 |height=600 }} {{#widget:Google Spreadsheet |key=0AlAK7TMhL37adDN3LUNlbV9saUxmdUh3MGMwRElXZnc |width=1000 |height=600 }} {{#widget:Google Spreadsheet |key=0AlAK7TMhL37adG5YODJmdkhIMnVZdTlVTGJDQVFIblE |width=1000 |height=600 }} {{#widget:Google Spreadsheet |key=0AlAK7TMhL37adGppR0NYd21SVHFQUFp1SFkya3M0TEE |width=1000 |height=600 }} {{#widget:Google Spreadsheet |key=0AlAK7TMhL37adHBlcGFGVFFHY0JRWmVTTzc1elJ0b0E |width=1000 |height=600 }} {{#widget:Google Spreadsheet |key=0AlAK7TMhL37adEdyVlRLVUp6aGxHWmlaUUhEemx0TEE |width=1000 |height=600 }} {{#widget:Google Spreadsheet |key=0AlAK7TMhL37adGxDeldqa29aSTJCN2s4LWZjZ1VGVHc |width=1000 |height=600 }} {{#widget:Google Spreadsheet |key=0AlAK7TMhL37adHpMZVU5ZUt6bDNsMzVoNXM5VjJEWlE |width=1000 |height=600 }} {{#widget:Google Spreadsheet |key=0AlAK7TMhL37adGZWeFlvUGMzeWNuWnQwLWVqeEJKMlE |width=1000 |height=600 }} {{#widget:Google Spreadsheet |key=0AlAK7TMhL37adHV3Ql8yU1hET3NoRkhBT0tDTXRyWUE |width=1000 |height=600 }}


Functions Used in Google Docs

Analysis

SJK 19:52, 21 December 2010 (EST)

19:52, 21 December 2010 (EST)
the Poisson distribution approaches normal for large expected number. So it's not necessarily true that the pre-amp aren't poisson distributed

The Histograms for "Pre-Amp" are normally distributed, not Poisson Distributed, and are, therefore, neglected in this analysis. I will also neglect 200ms since there appears to have been some sort of systematic error there.

[math]\displaystyle{ Sqrt(Mean) }[/math]

These are kept without correct sig. figs.

  • 800ms - 4.900674341
  • 400ms - 3.464383639
  • 100ms - 1.748891735
  • 80ms - 1.581833841
  • 40ms - 1.112394085
  • 20ms - 0.7864260932
  • 10ms - 0.5476779163

Deviation

These are copied out of the docs above

  • 800ms - 4.9339446
  • 400ms - 3.4119272
  • 100ms - 1.7646143
  • 80ms - 1.6206361
  • 40ms - 1.1476129
  • 20ms - 0.7775635
  • 10ms - 0.5459483

Difference

These are the values given to me by my caluculator

  • 800ms - 0.03327025865
  • 400ms - 0.05245643926
  • 100ms - 0.01572256521
  • 80ms - 0.03880225917
  • 40ms - 0.03521881515
  • 20ms - 0.0088625932
  • 10ms - 0.0017296163

The differences become more like those of a poisson distribution as the time interval decreases. This leads me to suspect that if we used an even smaller interval we would achieve an even greater similarity to a normal poisson distribution. I also notice that for the 100ms, 400ms, and 800ms the poisson distribution becomes like a gaussian, and is most likely no longer poisson distributed, but normally distributed.

SJK 20:06, 21 December 2010 (EST)

20:06, 21 December 2010 (EST)
Actually, all of your data look like Poisson! Poisson is approximately normal, as the expected number gets higher.

Thanks

  • To Dr. Steve Koch for helping me understand and evaluate my experiment.
  • To Katie for helping keep boredom away while we were collecting our data.
  • To Rickard T. Meyers for helping figuring out the steps we needed to analyze our data.
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