Random Integers?

Question

I am taking a statistics class. We are doing a presentation on how the TI-83 Calculator generates random integers. We need to come up with a formula or general rule on how the calculator comes up with the numbers. I know they aren't random, but I need to know how to get them myself.

Answer 1

Simple Random Sampling on TI 83
For the purpose of this example we will start by "seeding" the random number generator on the calculator. The reason we will do this is to ensure that your calculator gives the same numbers as mine. (Note: You generally do not need to do this unless instructed to do so.)

Seeding the Random Number Generator
At the home screen enter the seed ("12071941" for this example). Then press the STO> or "store" key which is next to 1. Then press the MATH key. Use the blue arrow keys to highlight PRB. The screen should look like figure 1.

figure 1 figure 2

Since "1:" is highlighted and that is the selection we want, you can press the ENTER key or the 1 key. This will cause the command to be displayed on the home screen looking like figure 2.

Pressing the ENTER key will cause the calculator to actually perform the command. You will know the calculator is finished when 12071941 displays on the next line. Press the MATH key and then the blue arrow keys to highlight PRB so the display looks like figure 1 again. Now press the 5 key and the screen will look like figure 3.

figure 3 figure 4

Now using the number keys and the comma key, which is above the 7, finish typing the line to look like figure 4. Then press the ENTER key to execute the command. The result will look like figure 5.

figure 5

The result contained in the curly braces is a set of 5 randomly selected integers between 1 and 20, inclusive. Notice that the integer 10 occurs twice, so that we have actually only selected 4 unique integers in the range. (In other words, we only have a simple random sample of size 4.)

Answer 2

A straightforward one is to use modular arithmetic, multiplying and adding a number repeatedly. For example, for a random number between 1 and 10, with a multiplier of 17 and adding 3. Note that both multiplier and adder need to be relatively prime to 10.

first number is 5 (chosen as the seed)
5 x 17 + 3 = 88. Next number is 8 (88 mod 10)
8 x 17 + 3 = 139. Next number is 9 (139 mod 10)
9 x 17 + 3 = 156, so the next number is 6 (156 mod 10)

and so on. This will create a repeating cycle after a while, but if you use bigger number (like your computer, which probably uses 2^32 = over 4 billion, you get a nice sequence of random numbers.

Get a long list of random numbers from your TI-83. You may be able to find the pattern on your own, using the above algorithm.

Answer 3

The random numbers on most calculators.. and those used for most computer programs... are actually Pseudo-Random... they are seemingly random.. but the same sequence of numbers can be reproduced over and over... using the same initial "seed" number...

why do they do this? so that it is possible for people to get the same results... very useful when one person encrypts something...and another has to decrypt it.