M 384C - Software

Here is a problem that you could work on before the class begins to get a bit of a head start with the software.

  1. Choose a continuous probability distribution with which you are not very familiar. (Perhaps the chi-square distribution or even something more exotic like the beta distribution.)

  2. Choose two or three values of the parameters.

  3. Use some mathematical software to graph the density function for each of those values of the parameters. (A plain spreadsheet is adequate.) Think about how the shape changes as the parameters change.

  4. Using your graph or your table of numerical values, find the value of x at which the density function is maximized.

  5. Use some statistical software to simulate drawing a sample of size 5000 from one of those distributions and then make a histogram of those values. Does the shape seem consistent with that you found when you graphed the density function? (If you don't have any statistical software, then you can't do this part yet. Some statistical software won't let you sample from a variety of distributions and so that software isn't useful here.)

  6. Redo the previous question with a sample of size 10,000. Does this improve your approximation to the graph of the density function?

Last updated April 10, 2011 . Mary Parker