1) Lets make a deal. This exercise is an example of a computer simulation. Read the text and work out the theoretical answer with others in your section. Repeat the game "switching" 10 times and "staying" 10 times and keep track of your results. Without further ado, let's play Lets Make a Deal courtesy of R. Webster West and Scott Street both of the Department of Statistics at The University of South Carolina. What is your estimate of the probability of winning when you switch, what is your estimate of the probability of winning when you don't switch? Note: you need to make sure that your browser is java-enabled (in Netscape click Edit>Preferences... and go to the advanced options menu and click "enable java" and "enable java script").
2) Discrete distribution: militia men. Click here and a SAS/Insight program will appear in your browser window. Click on "File>Save As..." in Netscape and choose "Format for Saved Document: Text" then click "OK". The program is now saved in your account (in your home directory, by default). The file's name is "lab4.sas". Return to this page by choosing "GO>Back" from the Netscape menu bar. To get started type "sas lab4 &" in one of the terminals open on your screen.
This data set does not represent a sample, it represents a probability distribution for the random variable 'Chest Size' of Scottish Militia men. Make a scatter plot of 'PROB' (y-axis) vs. 'SIZE,' this is a barplot (invisible bars!) of the distribution of chest size among Scottish militia men. Describe the distribution (symmetric, right or left skewed, unimodal or multi-modal). Calculate the mean and variance of the distribution. Be careful, calculating sample stats will not do it. Think about the formula for mean and variance and create a new column or two, then calculate summary statistics to obtain column sums.
Click on "File>End" on the SAS/Insight menu bar to quit the program.
3) Binomial Distribution. The following link is to a dynamic bar plot of binomial probabilities. You can change the "success" probability (pi) and the number of "trials" (n). Compare the shape (symmetric, right or left skewed) of the distribution a) fixing pi=0.5 and letting n=20 and n=10 and b) fixing n=20 and letting pi=0.1, 0.25, 0.75, and 0.9.Here is the link: binomial java script, courtesy of Balasubramanian Narasimhan of Stanford University.