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.
- 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.)
- Choose two or three values of the parameters.
- 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.
- Using your graph or your table of numerical values, find the value of x
at which the density function is maximized.
- 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.)
- Redo the previous question with a sample of size 10,000. Does this improve
your approximation to the graph of the density function?
April 10, 2011
. Mary Parker