Home » Archimedes archive » Acorn User » AU 1994-12.adf » !StarInfo_StarInfo » Craven/!Dice/!Help
Craven/!Dice/!Help
This website contains an archive of files for the Acorn Electron, BBC Micro, Acorn Archimedes, Commodore 16 and Commodore 64 computers, which Dominic Ford has rescued from his private collection of floppy disks and cassettes.
Some of these files were originally commercial releases in the 1980s and 1990s, but they are now widely available online. I assume that copyright over them is no longer being asserted. If you own the copyright and would like files to be removed, please contact me.
| Tape/disk: | Home » Archimedes archive » Acorn User » AU 1994-12.adf » !StarInfo_StarInfo |
| Filename: | Craven/!Dice/!Help |
| Read OK: | ✔ |
| File size: | 083D bytes |
| Load address: | 0000 |
| Exec address: | 0000 |
File contents
DICE SIMULATION PROGRAM D.Craven, Greenhead College, Huddersfield May 1994 The program is designed to illustrate properties of 3 common probability distributions, namely Uniform, Binomial and Geometric. It may be used as a classroom demonstration or for students to explore various aspects, perhaps in small groups. It is aimed primarily at 'A' levelmaths students, but some options may well be useful for other age groups. The software is simple to use,(see example below) and is mouse driven with some keyboard input. It is not multi-tasking, but should not interfere with other loaded software. All mouse buttons have the same effect. Points that can be illustrated include: 1. Basic properties of the given distribution, including mean and variance, shape and effect of parameter values (particularly for the Binomial Distribution). 2. The behaviour of random samples : several large samples can be observed ina short space of time 3. The improvement of the fit of a theoretical model to an observed data set as the sample size increases. This also includes the values of the sample mean and variance compared with those of the population. Example Double click on !Dice to start the program. Click anywhere within the GEOMETRIC DISTRIBUTION box. Type in 100 for the number of successes and press 'Return'. Select the number 6 only, then click on 'Done'. Note the shape of the distribution. This simulates the number of throws needed to get a six with a single die. Over a long run, you may expect to get a six once in every six throws : so why is the peak of the distribution not at 6? Click on the 'Show mean and variance' box and note the results. Click on the 'Repeat with new data' box and try 1000 successes. Note the smoother shape of the distribution. Click on 'show theoretical distribution' to compare the expected results withthose observed, and click on the same box again to flick back to your observed values. Try this comparison with different sample sizes, and note the relative valuesof the observed and theoretical mean and variance.
00000000 44 49 43 45 20 53 49 4d 55 4c 41 54 49 4f 4e 20 |DICE SIMULATION | 00000010 50 52 4f 47 52 41 4d 0a 44 2e 43 72 61 76 65 6e |PROGRAM.D.Craven| 00000020 2c 20 47 72 65 65 6e 68 65 61 64 20 43 6f 6c 6c |, Greenhead Coll| 00000030 65 67 65 2c 20 48 75 64 64 65 72 73 66 69 65 6c |ege, Huddersfiel| 00000040 64 0a 4d 61 79 20 31 39 39 34 0a 0a 0a 54 68 65 |d.May 1994...The| 00000050 20 70 72 6f 67 72 61 6d 20 69 73 20 64 65 73 69 | program is desi| 00000060 67 6e 65 64 20 74 6f 20 69 6c 6c 75 73 74 72 61 |gned to illustra| 00000070 74 65 20 70 72 6f 70 65 72 74 69 65 73 20 6f 66 |te properties of| 00000080 20 33 20 63 6f 6d 6d 6f 6e 20 70 72 6f 62 61 62 | 3 common probab| 00000090 69 6c 69 74 79 20 20 20 20 20 64 69 73 74 72 69 |ility distri| 000000a0 62 75 74 69 6f 6e 73 2c 20 6e 61 6d 65 6c 79 20 |butions, namely | 000000b0 55 6e 69 66 6f 72 6d 2c 20 42 69 6e 6f 6d 69 61 |Uniform, Binomia| 000000c0 6c 20 61 6e 64 20 47 65 6f 6d 65 74 72 69 63 2e |l and Geometric.| 000000d0 0a 49 74 20 6d 61 79 20 62 65 20 75 73 65 64 20 |.It may be used | 000000e0 61 73 20 61 20 63 6c 61 73 73 72 6f 6f 6d 20 64 |as a classroom d| 000000f0 65 6d 6f 6e 73 74 72 61 74 69 6f 6e 20 6f 72 20 |emonstration or | 00000100 66 6f 72 20 73 74 75 64 65 6e 74 73 20 74 6f 20 |for students to | 00000110 65 78 70 6c 6f 72 65 20 20 20 20 20 20 20 76 61 |explore va| 00000120 72 69 6f 75 73 20 61 73 70 65 63 74 73 2c 20 70 |rious aspects, p| 00000130 65 72 68 61 70 73 20 69 6e 20 73 6d 61 6c 6c 20 |erhaps in small | 00000140 67 72 6f 75 70 73 2e 20 20 49 74 20 69 73 20 61 |groups. It is a| 00000150 69 6d 65 64 20 70 72 69 6d 61 72 69 6c 79 20 61 |imed primarily a| 00000160 74 20 27 41 27 20 6c 65 76 65 6c 6d 61 74 68 73 |t 'A' levelmaths| 00000170 20 73 74 75 64 65 6e 74 73 2c 20 62 75 74 20 73 | students, but s| 00000180 6f 6d 65 20 6f 70 74 69 6f 6e 73 20 6d 61 79 20 |ome options may | 00000190 77 65 6c 6c 20 62 65 20 75 73 65 66 75 6c 20 66 |well be useful f| 000001a0 6f 72 20 6f 74 68 65 72 20 61 67 65 20 67 72 6f |or other age gro| 000001b0 75 70 73 2e 0a 0a 54 68 65 20 73 6f 66 74 77 61 |ups...The softwa| 000001c0 72 65 20 69 73 20 73 69 6d 70 6c 65 20 74 6f 20 |re is simple to | 000001d0 75 73 65 2c 28 73 65 65 20 65 78 61 6d 70 6c 65 |use,(see example| 000001e0 20 62 65 6c 6f 77 29 20 61 6e 64 20 69 73 20 6d | below) and is m| 000001f0 6f 75 73 65 20 64 72 69 76 65 6e 20 77 69 74 68 |ouse driven with| 00000200 20 20 20 73 6f 6d 65 20 6b 65 79 62 6f 61 72 64 | some keyboard| 00000210 20 69 6e 70 75 74 2e 20 49 74 20 69 73 20 6e 6f | input. It is no| 00000220 74 20 6d 75 6c 74 69 2d 74 61 73 6b 69 6e 67 2c |t multi-tasking,| 00000230 20 62 75 74 20 73 68 6f 75 6c 64 20 6e 6f 74 20 | but should not | 00000240 69 6e 74 65 72 66 65 72 65 20 77 69 74 68 20 20 |interfere with | 00000250 6f 74 68 65 72 20 6c 6f 61 64 65 64 20 73 6f 66 |other loaded sof| 00000260 74 77 61 72 65 2e 0a 41 6c 6c 20 6d 6f 75 73 65 |tware..All mouse| 00000270 20 62 75 74 74 6f 6e 73 20 68 61 76 65 20 74 68 | buttons have th| 00000280 65 20 73 61 6d 65 20 65 66 66 65 63 74 2e 0a 0a |e same effect...| 00000290 50 6f 69 6e 74 73 20 74 68 61 74 20 63 61 6e 20 |Points that can | 000002a0 62 65 20 69 6c 6c 75 73 74 72 61 74 65 64 20 69 |be illustrated i| 000002b0 6e 63 6c 75 64 65 3a 0a 0a 31 2e 20 42 61 73 69 |nclude:..1. Basi| 000002c0 63 20 70 72 6f 70 65 72 74 69 65 73 20 6f 66 20 |c properties of | 000002d0 74 68 65 20 67 69 76 65 6e 20 64 69 73 74 72 69 |the given distri| 000002e0 62 75 74 69 6f 6e 2c 20 69 6e 63 6c 75 64 69 6e |bution, includin| 000002f0 67 20 6d 65 61 6e 20 61 6e 64 20 76 61 72 69 61 |g mean and varia| 00000300 6e 63 65 2c 20 20 73 68 61 70 65 20 61 6e 64 20 |nce, shape and | 00000310 65 66 66 65 63 74 20 6f 66 20 70 61 72 61 6d 65 |effect of parame| 00000320 74 65 72 20 76 61 6c 75 65 73 20 28 70 61 72 74 |ter values (part| 00000330 69 63 75 6c 61 72 6c 79 20 66 6f 72 20 74 68 65 |icularly for the| 00000340 20 42 69 6e 6f 6d 69 61 6c 20 20 20 20 20 20 20 | Binomial | 00000350 20 20 20 44 69 73 74 72 69 62 75 74 69 6f 6e 29 | Distribution)| 00000360 2e 0a 0a 32 2e 20 54 68 65 20 62 65 68 61 76 69 |...2. The behavi| 00000370 6f 75 72 20 6f 66 20 72 61 6e 64 6f 6d 20 73 61 |our of random sa| 00000380 6d 70 6c 65 73 20 3a 20 73 65 76 65 72 61 6c 20 |mples : several | 00000390 6c 61 72 67 65 20 73 61 6d 70 6c 65 73 20 63 61 |large samples ca| 000003a0 6e 20 62 65 20 6f 62 73 65 72 76 65 64 20 69 6e |n be observed in| 000003b0 61 20 73 68 6f 72 74 20 73 70 61 63 65 20 6f 66 |a short space of| 000003c0 20 74 69 6d 65 0a 0a 33 2e 20 54 68 65 20 69 6d | time..3. The im| 000003d0 70 72 6f 76 65 6d 65 6e 74 20 6f 66 20 74 68 65 |provement of the| 000003e0 20 66 69 74 20 6f 66 20 61 20 74 68 65 6f 72 65 | fit of a theore| 000003f0 74 69 63 61 6c 20 6d 6f 64 65 6c 20 74 6f 20 61 |tical model to a| 00000400 6e 20 6f 62 73 65 72 76 65 64 20 64 61 74 61 20 |n observed data | 00000410 73 65 74 20 61 73 20 74 68 65 20 73 61 6d 70 6c |set as the sampl| 00000420 65 20 73 69 7a 65 20 69 6e 63 72 65 61 73 65 73 |e size increases| 00000430 2e 20 20 54 68 69 73 20 61 6c 73 6f 20 69 6e 63 |. This also inc| 00000440 6c 75 64 65 73 20 74 68 65 20 76 61 6c 75 65 73 |ludes the values| 00000450 20 6f 66 20 74 68 65 20 73 61 6d 70 6c 65 20 20 | of the sample | 00000460 20 6d 65 61 6e 20 61 6e 64 20 76 61 72 69 61 6e | mean and varian| 00000470 63 65 20 63 6f 6d 70 61 72 65 64 20 77 69 74 68 |ce compared with| 00000480 20 74 68 6f 73 65 20 6f 66 20 74 68 65 20 70 6f | those of the po| 00000490 70 75 6c 61 74 69 6f 6e 2e 0a 0a 0a 45 78 61 6d |pulation....Exam| 000004a0 70 6c 65 0a 0a 44 6f 75 62 6c 65 20 63 6c 69 63 |ple..Double clic| 000004b0 6b 20 6f 6e 20 21 44 69 63 65 20 74 6f 20 73 74 |k on !Dice to st| 000004c0 61 72 74 20 74 68 65 20 70 72 6f 67 72 61 6d 2e |art the program.| 000004d0 0a 0a 43 6c 69 63 6b 20 61 6e 79 77 68 65 72 65 |..Click anywhere| 000004e0 20 77 69 74 68 69 6e 20 74 68 65 20 47 45 4f 4d | within the GEOM| 000004f0 45 54 52 49 43 20 44 49 53 54 52 49 42 55 54 49 |ETRIC DISTRIBUTI| 00000500 4f 4e 20 62 6f 78 2e 0a 54 79 70 65 20 69 6e 20 |ON box..Type in | 00000510 31 30 30 20 66 6f 72 20 74 68 65 20 6e 75 6d 62 |100 for the numb| 00000520 65 72 20 6f 66 20 73 75 63 63 65 73 73 65 73 20 |er of successes | 00000530 61 6e 64 20 70 72 65 73 73 20 27 52 65 74 75 72 |and press 'Retur| 00000540 6e 27 2e 0a 53 65 6c 65 63 74 20 74 68 65 20 6e |n'..Select the n| 00000550 75 6d 62 65 72 20 36 20 6f 6e 6c 79 2c 20 74 68 |umber 6 only, th| 00000560 65 6e 20 63 6c 69 63 6b 20 6f 6e 20 27 44 6f 6e |en click on 'Don| 00000570 65 27 2e 0a 4e 6f 74 65 20 74 68 65 20 73 68 61 |e'..Note the sha| 00000580 70 65 20 6f 66 20 74 68 65 20 64 69 73 74 72 69 |pe of the distri| 00000590 62 75 74 69 6f 6e 2e 0a 0a 54 68 69 73 20 73 69 |bution...This si| 000005a0 6d 75 6c 61 74 65 73 20 74 68 65 20 6e 75 6d 62 |mulates the numb| 000005b0 65 72 20 6f 66 20 74 68 72 6f 77 73 20 6e 65 65 |er of throws nee| 000005c0 64 65 64 20 74 6f 20 67 65 74 20 61 20 73 69 78 |ded to get a six| 000005d0 20 77 69 74 68 20 61 20 73 69 6e 67 6c 65 20 64 | with a single d| 000005e0 69 65 2e 20 20 20 4f 76 65 72 20 61 20 6c 6f 6e |ie. Over a lon| 000005f0 67 20 72 75 6e 2c 20 79 6f 75 20 6d 61 79 20 65 |g run, you may e| 00000600 78 70 65 63 74 20 74 6f 20 67 65 74 20 61 20 73 |xpect to get a s| 00000610 69 78 20 6f 6e 63 65 20 69 6e 20 65 76 65 72 79 |ix once in every| 00000620 20 73 69 78 20 74 68 72 6f 77 73 20 3a 20 73 6f | six throws : so| 00000630 20 20 20 77 68 79 20 69 73 20 74 68 65 20 70 65 | why is the pe| 00000640 61 6b 20 6f 66 20 74 68 65 20 64 69 73 74 72 69 |ak of the distri| 00000650 62 75 74 69 6f 6e 20 6e 6f 74 20 61 74 20 36 3f |bution not at 6?| 00000660 0a 43 6c 69 63 6b 20 6f 6e 20 74 68 65 20 27 53 |.Click on the 'S| 00000670 68 6f 77 20 6d 65 61 6e 20 61 6e 64 20 76 61 72 |how mean and var| 00000680 69 61 6e 63 65 27 20 62 6f 78 20 61 6e 64 20 6e |iance' box and n| 00000690 6f 74 65 20 74 68 65 20 72 65 73 75 6c 74 73 2e |ote the results.| 000006a0 0a 43 6c 69 63 6b 20 6f 6e 20 74 68 65 20 27 52 |.Click on the 'R| 000006b0 65 70 65 61 74 20 77 69 74 68 20 6e 65 77 20 64 |epeat with new d| 000006c0 61 74 61 27 20 62 6f 78 20 20 61 6e 64 20 74 72 |ata' box and tr| 000006d0 79 20 31 30 30 30 20 73 75 63 63 65 73 73 65 73 |y 1000 successes| 000006e0 2e 20 20 4e 6f 74 65 20 74 68 65 20 20 20 73 6d |. Note the sm| 000006f0 6f 6f 74 68 65 72 20 73 68 61 70 65 20 6f 66 20 |oother shape of | 00000700 74 68 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e |the distribution| 00000710 2e 0a 43 6c 69 63 6b 20 6f 6e 20 27 73 68 6f 77 |..Click on 'show| 00000720 20 74 68 65 6f 72 65 74 69 63 61 6c 20 64 69 73 | theoretical dis| 00000730 74 72 69 62 75 74 69 6f 6e 27 20 74 6f 20 63 6f |tribution' to co| 00000740 6d 70 61 72 65 20 74 68 65 20 65 78 70 65 63 74 |mpare the expect| 00000750 65 64 20 72 65 73 75 6c 74 73 20 77 69 74 68 74 |ed results witht| 00000760 68 6f 73 65 20 6f 62 73 65 72 76 65 64 2c 20 61 |hose observed, a| 00000770 6e 64 20 63 6c 69 63 6b 20 6f 6e 20 74 68 65 20 |nd click on the | 00000780 73 61 6d 65 20 62 6f 78 20 61 67 61 69 6e 20 74 |same box again t| 00000790 6f 20 66 6c 69 63 6b 20 62 61 63 6b 20 74 6f 20 |o flick back to | 000007a0 79 6f 75 72 20 20 20 20 20 20 20 20 6f 62 73 65 |your obse| 000007b0 72 76 65 64 20 76 61 6c 75 65 73 2e 0a 54 72 79 |rved values..Try| 000007c0 20 74 68 69 73 20 63 6f 6d 70 61 72 69 73 6f 6e | this comparison| 000007d0 20 77 69 74 68 20 64 69 66 66 65 72 65 6e 74 20 | with different | 000007e0 73 61 6d 70 6c 65 20 73 69 7a 65 73 2c 20 61 6e |sample sizes, an| 000007f0 64 20 6e 6f 74 65 20 74 68 65 20 72 65 6c 61 74 |d note the relat| 00000800 69 76 65 20 76 61 6c 75 65 73 6f 66 20 74 68 65 |ive valuesof the| 00000810 20 6f 62 73 65 72 76 65 64 20 61 6e 64 20 74 68 | observed and th| 00000820 65 6f 72 65 74 69 63 61 6c 20 6d 65 61 6e 20 61 |eoretical mean a| 00000830 6e 64 20 76 61 72 69 61 6e 63 65 2e 0a |nd variance..| 0000083d
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