Barry Kissane
19
LONGRUN
Purpose
To illustrate what happens in the long run when events with a certain probability are
generated. For example, to see what happens when a fair coin is tossed repeatedly, by
plotting the proportion of the heads after various numbers of tosses.
Operation
Enter the probability concerned and press to continue.
The program will display the 'ideal' theoretical probability as a horizontal line. The
vertical axis is marked in steps of 0.1 or 10%.
After each simulated event, the proportion of 'successful' times is plotted. This is likely
to be eventually (in the long run) close to the horizontal line.
After a screen full of simulations, the relative frequency is displayed. This will not
usually be the same as the probability.
Press the key to switch between the graph and the numerical results.
Press the key to repeat the simulation.
Do this a few times to see how much it varies each time. Compare your results with
someone else's.
There is a discussion of the use of this sort of program in the text,
Kissane, Barry, Harradine, Anthony & Boys, Anthony (1999) Mathematical Interactions:
Data Analysis and Probability, Chatswood, NSW: Shriro, pp 21-22.
