# Physics307L:People/Mondragon/Poisson

The desire to perform these experiments arose from arguments about how accurately a Poisson probability distribution could fit data that should most probably follow the Poisson distribution. One thing I see immediately is that the Poisson distribution can not fit data collected from a finite number of counting experiments **exactly** but as the number of counting experiments preformed approaches infinity, the data should fit the distribution more and more tightly.

I will be using the **poissrnd()** function included in Gnu Octave vers. 3.0.0 to generate random numbers with a Poisson distribution with parameter **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \lambda}**
. Gnu Octave is open source, so it shouldn't be too difficult to find the source code and examine how these numbers are generated for those who are curious. I am using this number generator to model counting experiments.

Things I want to do:

- using the Poisson random number generator, generate
**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle n}**numbers using parameter**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \lambda_0}**and quantify- how well a Poisson distribution with parameter
**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \lambda_0}**fits the generated data and how this varies with - what parameter for the Poisson distribution best fits the generated data and find a standard deviation for how much the parameter varies

- how well a Poisson distribution with parameter
- repeat the above but with different . Try to find a relationship between , , and
- for data generated with parameters and , find how accurate are the Poisson distribution's predictions of what the count frequency for count number is, and how this varies with , , and

For the test on how accurate the overall fit is, the dependent variable is and the independent variables are and . For the test of the accuracy of the distribution's predictions about the frequency of a count number, the dependent variable is and the independent variables are , and .

This is to be the main branch page

From here, access