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This program is designed for use when students are investigating the concept of Bernoulli Trials in probability. The user nominates how many trials to perform, what the probability of success is and the program reports how many successes were found. The results can be stored into L0 if desired. 
If a graphical representation is needed then the user can go to the HOME view and STO L0 into one of the Statistics aplet columns. The default choice is to discard the results, which will empty L0.

Hands of Cards 
For experimental probability problems involving cards, this program will create and record any number of 'hands' of cards of any specified size.  For example, if 10 poker hands were needed then the results are shown right.
The results are stored in M0 and, because matrices can't handle text, it is not possible to display "King of Hearts" in the results. A code is used instead, where the hundreds digit indicates the suit (100=Clubs, 200=Diamonds, 300=Hearts & 400=Spades) and the tens & units digits indicate the card value.
For example, an entry of 304 would be a 4 of Hearts, while 212 would be a Queen of Diamonds.

Note: The results are stored in matrix M0, which is not deleted at the end of the program. To save memory it is worth deleting it when it is no longer needed.

Long Run Prob 
Students generally accept as being reasonable that the more experiments you perform, the more closely the experimental probability approaches the theoretical probability.  This program is designed to show this visually.  The user nominates a probability and a number of trials and the program then displays the values of the experimental probability as it changes with the number of trials. Visually it becomes quite clear that the values are converging and also, more importantly, that the values are wildly different for small numbers of trials.
The dotted line on the graph shows the theoretical probability value and the experimental probability is displayed at the top of the screen as it changes.

Random Numbers 
This program generates set of random numbers, either integers or decimals.  The results are stored into either a list (L1...L5) or a column of the Statistics aplet (C1...C5).

Avg Run Length 
The concept of average run length is often useful in attempting to detect forgery of results. For example, if a student were given the task of tossing a coin 200 times for homework and decided to fake the results, they will often produce a fake which is 'too random'.  Although people understand intellectually that it is possible to have runs of heads or tails, they usually don't take this into account in their forgery. Investigating the average run length will often show a value which is lower than the expected value of 0.5/[p(1-p)].

For example, suppose the student submitted 30 tosses of:
            T H T H H T H T H H T H H T H T H T T T H T H T T H H T H T
The probability of an H according to this run is 0.5 exactly as expected, but what of the run length?
Breaking this into 'runs' gives: T,H,T,HH,T,H,T,HH,T,HH,T,H,T,H,TTT,H,T,H,T,T,HH,T,H,T
This gives runs of: 1,1,1,2,1,1,1,2,1,2,1,1,1,1,3,1,1,1,1,1,2,1,1,1 giving an average run length of  30/24 or 1.25. 

The expected value is 0.5/[0.5*(1-0.5)] or 2. From this one might suspect that the sample was faked, although the sample size is clearly too small to be sure.

An interesting class investigation can be performed by having each student perform an experiment like tossing a coin 200 times and privately giving instructions to some students to fake their results, without mentioning the concept of run length.  Once all the results are in, the class can be told that some students faked their results (but not who or how many) and seeing if they can use run length to identify who they were.

This program allows the student to investigate average run length by having the computer 'toss the coins' (for any given probability of sucess & number of trials) and give the average run length it finds.  The program reports its ongoing results as the trials progress as well as the final totals.  Change to the NUM view to see the actual run lengths recorded.
If this experiment is recorded repeatedly and the results are stored in columns C2 and C3 (C1 is used by the program) as ordered pairs of (prob, length) then they can be graphed as bivariate data with a view to investigating and finding the rule of 0.5/[p(1-p)].

Note: Column C1 of the Statistics aplet is overwritten by this program and some settings of the aplet may be changed.

This program simulates a 'spinner' and allows the student to collect experimental results.
The spinner can have any number of segments and these segments can be either equally spaced or their sizes can be specified in degrees.
To spin, press any key.  When you press ENTER the program will terminate.

Overlay Normal 
It is often very helpful to be able to overlay a normal curve with the same mean and standard deviation over the top of an existing histogram.
As the instructions say, there are certain things that MUST be done before running the program.
This means hold down the ON button and, while still holding it down, press PLOT.
bulletThe data must be graphed in the PLOT view.
bulletThe image must be captured for use by pressing ON+PLOT
bulletIn the NUM view, press STATS so that the values of the mean and standard deviation can be calculated. If this is done then the program will automatically import them when it is run.

The image of the PLOT view is then redisplayed and the equivalent normal curve is superimposed and displayed until any key is pressed.

This is something that is easily done in the HOME view but if you're lazy, this will do it for you.
The program will only run successfully if the data has been graphed in the PLOT view first and the FIT line graphed (press MENU & FIT).

Last modified: 19 Dec 2007                                             Sitemap        Home        Contact Me