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

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{| border="1" cellpadding="20" cellspacing="0"
 
{| border="1" cellpadding="20" cellspacing="0"
−
! colspan="2"|Plateau Zeroing
+
! colspan="2"|Angular Distribution
 
|-
 
|-
 
|Time Start
 
|Time Start
 
|Time Stop
 
|Time Stop
−
|Time elapsed (min.)
+
|Time elapsed (min.; hour)
 
|Thresholds on both Scintillators
 
|Thresholds on both Scintillators
 
|Singles Count (on top)
 
|Singles Count (on top)
 
|Coinc. Counts
 
|Coinc. Counts
 
|Coinc. per minute
 
|Coinc. per minute
 +
|Coinc. per Hour
 
|Angle measure
 
|Angle measure
 
|-
 
|-
 
|1:35 pm on 8/31
 
|1:35 pm on 8/31
 
|1:10 pm on 9/04
 
|1:10 pm on 9/04
−
|5725 min
+
|5725 min; 95.42 hr
 
|225
 
|225
 
|626816
 
|626816
 
|1654
 
|1654
 
|.2889
 
|.2889
 +
|17.33
 
|75 degrees
 
|75 degrees
 
|}<br>
 
|}<br>
  
−
;Binomial distribtuion
+
Cosmic rates measured each hour when the telecope accepts cosmics which intersect the earth's surface perpendicularly (defined as zero degrees).
−
: best example is a coin toss, its either heads or tails
 
−
: mean (<math>\mu</math>) = number of tries <math>n</math>(coin flips) * probability of success<math>p</math> (head, 1/2)
 
−
:standard deviation(<math>\sigma</math>) = <math>np(1-p)</math>
 
−
 
 
−
; Poisson Distribution
 
−
: standard deviation (<math>\sigma</math>) = root of the mean (<math>\sqrt{\mu}</math>)
 
−
: use in counting experiments
 
−
: 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.
 
−
: In the cosmic ray telescope experiment the mean number of detected cosmic rays is much smaller than the number of cosmic rays passing by.
 
−
 
 
−
;Gaussian/Normal Distribution
 
−
: Full WIdth at Half Max (FWHM) = width of the distribution at half the value of the maximum probabilty (distibution peak) = <math>\Gamma</math>
 
−
:standard deviation (<math>\sigma</math>) = <math>\frac{\Gamma} {2.354}</math>
 
−
:error = <math>0.675 \sigma</math>
 
−
 
 
 
{| border="1" cellpadding="20" cellspacing="0"
 
{| border="1" cellpadding="20" cellspacing="0"
 
|-
 
|-
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|Coinc. per hour
 
|Coinc. per hour
 
|<math>\sqrt{N}</math>
 
|<math>\sqrt{N}</math>
−
|<math>(x_i-\bar{x})^2</math>
+
|<math>\sqrt{(x_i-\bar{x})^2}</math>
 
|-
 
|-
−
|1:20 pm || 2:20 pm ||1 ||5694 ||127 || 127 || 11.3 ||121
+
|1:20 pm || 2:20 pm ||1 ||5694 ||127 || 127 || 11.3 ||11
 
|-
 
|-
−
|2:20 pm || 3:20 pm ||1 ||4896 ||136 || 136 || 11.6 ||4
+
|2:20 pm || 3:20 pm ||1 ||4896 ||136 || 136 || 11.6 ||2
 
|-
 
|-
−
|3:20 pm || 4:20 pm ||1 ||4655 ||151 || 151 || 12.2 ||169
+
|3:20 pm || 4:20 pm ||1 ||4655 ||151 || 151 || 12.2 ||13
 
|}<br>
 
|}<br>
  
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Instrumental Uncertainty =<math>\sigma = \sqrt{\frac{\sum (x_i - \bar{x})^2}{N-1}} = 12.12</math> 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 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.
+
The cosmic ray telescope counting experiment appears to be following Poisson statistics.
 +
[http://www.iac.isu.edu/mediawiki/index.php/Statistics_for_Experimenters See Statistics for Experimentalists]

Latest revision as of 21:42, 19 September 2007

Angular Distribution
Time Start Time Stop Time elapsed (min.; hour) Thresholds on both Scintillators Singles Count (on top) Coinc. Counts Coinc. per minute Coinc. per Hour Angle measure
1:35 pm on 8/31 1:10 pm on 9/04 5725 min; 95.42 hr 225 626816 1654 .2889 17.33 75 degrees


Cosmic rates measured each hour when the telecope accepts cosmics which intersect the earth's surface perpendicularly (defined as zero degrees).

Time Start Time Stop Time elapsed (hour) Singles Count (on top) Coinc. Counts Coinc. per hour [math]\sqrt{N}[/math] [math]\sqrt{(x_i-\bar{x})^2}[/math]
1:20 pm 2:20 pm 1 5694 127 127 11.3 11
2:20 pm 3:20 pm 1 4896 136 136 11.6 2
3:20 pm 4:20 pm 1 4655 151 151 12.2 13


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

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

The cosmic ray telescope counting experiment appears to be following Poisson statistics. See Statistics for Experimentalists

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