Reference no: EM13807724

Your program should use the Free Pascal compiler described in CSC 540. When you hand in your assignment to the digital dropbox, it should be a .PAS file, not zipped.

Your assignment is to explore the behavior of your Pascal random number generator by throwing random numbers between 20001 and 380000 (inclusive). At first you will bin the results into 10 equal histogram bins. After each simulation run (more about that below), output the histogram results into a text file. Then import the text file into Excel (or some other graphing program) and use a bar graph to display your histogram results. If you don't know what a histogram is, check the web. Here is one web resource: https://deming.eng.clemson.edu/pub/tutorials/qctools/histm.htm

You should run at least three different simulations to generate numbers to put into your histogram bins. Feel free to do more simulations than this (you might find that interesting), but you MUST do these. It might be useful to do each of these more than once and, using the Free Pascal function randomize, see if different runs give different results.

1. Throw 1,000 numbers, and output the histogram numbers.
2. Throw 10,000 numbers, and output the histograms.
3. Throw 100,000 numbers, and output the histograms.

Now you will do a similar simulation, but with more numbers and a more interesting kind of graph. This time instead of doing 6 bins in your histogram, do 36 bins. And instead of displaying a one dimensional histogram, make a TWO dimensional histogram in 6 rows of 6. (This is something like a reduced size chess board.) This is easy to do with MS Excel. Here are the next "runs" you should do:

4. Throw 100,000 numbers, and output the histogram numbers.
5. Throw 1,000,000 numbers, and output the histogram numbers.
6. Throw 10,000,000 numbers, and output the histogram numbers.

Be careful to use qword instead of int variables for the appropriate declarations since some of these numbers will be way over 32,767 (the limit of a Pascal int). NOTE WELL: when you are doing histograms, you do NOT need to store the numbers that are generated. You only need to keep track of the counts in the bins. If you try to keep all the numbers you generate, you are going to have BIG problems. Also, make sure that your bins are assigned in such a way that a random choice from the range is equally likely to land in any of the bins. (Notice that 10 and 36 both divide evenly into 360000, the number of different numbers that you can throw.)

Also, while you are debugging your program, it is wise to print out to the screen now and then so you can see what's going on (and perhaps what's going wrong!). But once you start running programs that do LOTS of calculations, then do input and output sparingly; input and output require FAR more time than other calculations, and you want simulations doing millions of trials to go quickly, not slowly.

As you gather results, think about the law of large numbers and how that affects your results. What do you expect to happen, and what actually does happen? How do you explain the difference?