NOTE: An Excel file with the Rutherford/Geiger Poisson example that we looked at in class can be found here.

For determining the half-lives of radioactive isotopes, it is important to know what the background radiation is for a given detector over a certain period. A gamma-ray detection experiment over 300 one-second intervals yielded the data (x_observed) at the link below. The researcher wants to know if a Poisson RV is a good model for the data, and if so what the parameter should be for the Poisson distribution.

• 300 observations as a column of data in a text file that can be pasted into Excel

For the questions below, copy and paste the appropriate output from Excel into Word.

(a) Find the frequencies of 0,1,2,...,8 in the observed data. These are the observed counts.
If you are using JMP, you will want to use the observed data with the ordinal modeling type for this part.

(b) Calculate the sample mean and sample variance. How do these two statistics compare to each other?
What is your estimate of the Poisson parameter based on these data (round your answer to the nearest tenth)?
If you are using JMP, you will want to use the observed data with the continuous modeling type for this part.

(c) Use Excel to determine the expected counts based on your Poisson probability model.

(d) Draw a graph of the probability histogram for the Poisson RV with your estimated parameter.

         This link has info on drawing a probability histogram for a PMF in Excel.

(e) Draw a graph of the relative frequency histogram for the observed data (x_obs).

         This link has info on drawing a relative frequency histogram for some observed data in Excel.