September 4, 2007 - Cosmic Telescope

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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


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
standard deviation[math]\sigma[/math] = Half Width [math]\Gamma[/math] / 2.354
error = [math]2\ln(2) \sigma[/math]
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.