September 4, 2007 - Cosmic Telescope: Difference between revisions

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]\displaystyle{ \sqrt{N} }[/math]	[math]\displaystyle{ (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]\displaystyle{ \mu }[/math] = 138 counts per hour

Instrumental Uncertainty =[math]\displaystyle{ \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]\displaystyle{ \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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 |75 degrees
 |}<br>
-;Binomial distribtuion
-: 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>
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 The cosmic ray telescope sounting experiment appears to be following Poisson statistics.
+[http://www.iac.isu.edu/mediawiki/index.php/Statistics_for_Experimenters See Statistics ofr Experimentalists]