# Statistics for Experimenters

# Definitions

- Accuracy
- A measure of how close the experimental result is to the "true" value

- Precisison
- 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 ( ) = number of tries (coin flips) * probability of success (head, 1/2)
- standard deviation( ) =

- Poisson Distribution
- standard deviation ( ) = root of the mean ( )
- 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

where

- = number of occurances
- = mean

- Gaussian/Normal Distribution
- Full WIdth at Half Max (FWHM) = width of the distribution at half the value of the maximum probabilty (distibution peak) =
- standard deviation ( ) =
- error =