Difference between revisions of "September 4, 2007 - Cosmic Telescope"

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|75 degrees
 
|75 degrees
 
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;Binomial distribtuion
 
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: best example is a coin toss, its either heads or tails
 
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: mean (<math>\mu</math>) = number of tries <math>n</math>(coin flips) * probability of success<math>p</math> (head, 1/2)
 
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:standard deviation(<math>\sigma</math>) = <math>np(1-p)</math>
 
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; Poisson Distribution
 
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: standard deviation (<math>\sigma</math>) = root of the mean (<math>\sqrt{\mu}</math>)
 
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: use in counting experiments
 
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: the distribtuion approximates the Binomial Distribution for the special case when the mean (<math>\mu</math>) is a lot less than the number of attempts to measure (<math>n</math>) because the probability of the event occurrring is small.
 
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: In the cosmic ray telescope experiment the mean number of detected cosmic rays is much smaller than the number of cosmic rays passing by.
 
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;Gaussian/Normal Distribution
 
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: Full WIdth at Half Max (FWHM) = width of the distribution at half the value of the maximum probabilty (distibution peak) = <math>\Gamma</math>
 
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:standard deviation (<math>\sigma</math>) = <math>\frac{\Gamma} {2.354}</math>
 
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:error = <math>0.675 \sigma</math>
 
  
 
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The cosmic ray telescope sounting experiment appears to be following Poisson statistics.
 
The cosmic ray telescope sounting experiment appears to be following Poisson statistics.
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[http://www.iac.isu.edu/mediawiki/index.php/Statistics_for_Experimenters See Statistics ofr Experimentalists]

Revision as of 16:16, 5 September 2007

Plateau Zeroing
Time Start Time Stop Time elapsed (min.) Thresholds on both Scintillators Singles Count (on top) Coinc. Counts Coinc. per minute Angle measure
1:35 pm on 8/31 1:10 pm on 9/04 5725 min 225 626816 1654 .2889 75 degrees


Time Start Time Stop Time elapsed (hour) Singles Count (on top) Coinc. Counts Coinc. per hour [math]\sqrt{N}[/math] [math](x_i-\bar{x})^2[/math]
1:20 pm 2:20 pm 1 5694 127 127 11.3 121
2:20 pm 3:20 pm 1 4896 136 136 11.6 4
3:20 pm 4:20 pm 1 4655 151 151 12.2 169


Mean [math]\mu[/math] = 138 counts per hour

Instrumental Uncertainty =[math]\sigma = \sqrt{\frac{\sum (x_i - \bar{x})^2}{N-1}} = 12.12[/math] counts per hour

Your instrumental uncertainty is approximately equal to the Poisson sigma ([math]\sqrt{138}= 11.7[/math]) counts per hour.

The cosmic ray telescope sounting experiment appears to be following Poisson statistics. See Statistics ofr Experimentalists

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