Poisson Statistics
Background
The Poisson distribution can characterize random events that occur at a well-defined average rate. It is widely used in atomic and sub-atomic physics. The Poisson distribution is effective in a variety of statistical applications. The most common involve event probabilities, but several assumptions must hold true: i) the rate at which random events occur does not change for the duration of the measurement; ii) the occurrence of one event does not change the likelihood of another event; iii) events occur at a slow enough rate that they can be individually distinguished.
In this experiment, Poisson statistics will be used to analyze random radioactive decay events that occur in a defined time interval. A decay occurs an integer k number of times in the interval, including possibly not at all Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): \hat{S} = \hat{\sigma}_+ +\hat{\sigma}_- . The average number of events expected in a defined time interval is λ, known as the event rate. Given λ, the probability of observing k events in the time interval is :
Background Reading
History
Experiment set up and verified by Martin Hoeferkamp, January 2020
