Statistics for Experimenters

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A measure of how close the experimental result is to the "true" value
A meauser of close the result is determined without knowing the true vaule
Precision is often used to predict the accuracy of a quantity to be measured (you don't know the answer before doing the experiment)

Random Error
The error in a result due to the finite precision of an experiment
A measure of the statistical fluctuations which result after repeated experimentation
Systematic Error
Reproducable inaccuracies introduced by faulty equipment, calibration, or technique.

Probability Distributions

Binomial distribtuion
random, independent process with two possible outcomes
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 probability of the event occuring 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.

The probability distribution is given as

[math]P(k,\mu) = \frac{\mu^{k}e^{-\mu}}{k!}[/math]


[math]k[/math] = number of occurances
[math]\mu[/math] = mean
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 \sqrt{2 \ln 2}} = \frac{\Gamma} {2.354}[/math]
error = [math]0.675 \sigma[/math]