SimuLab 3: Wholesale Coin Flipping

Random Walk is a program that uses a computer to do our ten-penny flip thousands of times faster than we can. The computer is programmed so that "heads'' and "tails'' are equally likely to occur. The computer also plots the results. Please see Java Applet Page.

1. Start the Random Walk program, which begins with the coin-flipping game (Figure 3.3)


2. Click on the Flip button to flip one coin at a time. Click Flip again. And again. Repeat until you have flipped ten coins. Study the numbers at the bottom and the top of the graph: What is being recorded?


3. Now repeat the process, but this time click Go to have the computer flip coins automatically, one after the other. Notice that as the bar graph (histogram) grows, the vertical scale changes to keep the plot on the screen. The computer will run 100 trials of ten coins each. Record results in your notebook.


4. Now choose a new window (choose Coin Flip in the New box on the control panel).


5. Click Go and watch the graph grow. To speed up the process, choose Less Graphics from the Options menu.


6. Choose the Tile Windows command under the Options menu and compare the two graphs. (Tile Windows shrinks the windows and places them side by side, so you can view more than one at a time.) Are the two patterns the same? Can you predict the shape of the next graph if you make a third run? Try it! Tile the resulting three displays.


7. Click on Coin Flip one more time, select 500 for the Number of Trials under the Experiment menu, and choose Less Graphics under the Options menu. Press Go.


8. Select the Tile Windows command under Options to see all of these results side by side on the screen.


9. Experiment on your own. Change the number of trials. You can also change the number of flips per trial with the Number of Steps command under the Experiment menu. You should now be able to verify the prediction you made at the end of HandsOn 10. Again, make a prediction about what the graph will look like.

                   

Q3.12: As the number of trials increases how does the shape of the graph change? Is the width of the distribution greater after a larger number of trials? Is the bar graph smoother after 500 trials than after 100 trials?

    

Q3.13: Does the number of trials or the number of flips affect the shape of the graph? How?