Question 5.61

5.61 Simulating Poisson counts.

Most statistical software packages can randomly generate Poisson counts for a given . In this exercise, you will generate 1000 Poisson counts for .

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  • JMP users: With a new data table, right-click on header of Column 1 and choose Column Info. In the drag down dialog box named Column Properties, pick the Formula option. You will then encounter a Formula dialog box. Find and click in the Random Poisson function into the dialog box. Proceed to give the mean value of 9, which JMP refers to as “lambda.” Click OK twice to return to the data table. Finally, right-click on any cell of the column holding the formula, and choose the option of Add Rows. Input a value of 1000 for the number of rows to create and click OK. You will find 1000 random Poisson counts generated.
  • Minitab users: Calc → Random Data → Poisson. Enter 1000 in the Number of row of data to generate dialog box, type “c1” in the Store in column(s) dialog box, and enter 9 in the Mean dialog box. Click OK to find the random Poisson counts in column c1.
  1. Produce a histogram of the randomly generated Poisson counts, and describe its shape.
  2. What is the sample mean of the 1000 counts? How close is this simulation estimate to the parameter value?
  3. What is the sample standard deviation of the 1000 counts? How close is this simulation estimate to the theoretical standard deviation?

5.61

Software, answers will vary. (a) The shape should be roughly symmetric. (b) The mean should be close to 9. (c) The standard deviation should be close to .