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TwoExcelsWork.zip

Excel_DataTablesHistogramsDistributions.xlsx

Histogram

Set F to the number of random draws that you with to sum together.
You can observe the distribution that emerges on the right.
At F=1, you see that values are just uniformly distributed.
At F=12, you can clearly see the normal distribution emerge out of randomness.
F
12
F_Row 1 2 3 4 5 6 7 8 9 10 11 12 Bins CDF PDF
n Sum 0 0 0 0
1 7.5577784253 0.8756215053 0.5306070002 0.6095219924 0.4284170464 0.4819382718 0.789155995 0.1264789934 0.5313854892 0.9908442965 0.735583903 0.7311198959 0.7271040361 0.05 0.6 0 0
2 7.7503565562 0.242723613 0.7394091502 0.5471630057 0.1717074073 0.4154429024 0.7817748151 0.9901155486 0.9632869101 0.4387185484 0.8916502376 0.862832308 0.7055321099 0.1 1.2 0 0
3 6.1672008511 0.2077704902 0.5833045206 0.6254222247 0.8552758347 0.1329172889 0.6520643635 0.8300749711 0.2527108126 0.8796978644 0.7365863397 0.1939251412 0.2174509995 0.15 1.8 0 0
4 6.8133322298 0.2005928101 0.9634120663 0.2597987799 0.992280245 0.1572697629 0.930937473 0.9241416206 0.4137567414 0.9430397978 0.2473700095 0.6164865844 0.164246339 0.2 2.4 0 0
5 3.9372718855 0.3371685413 0.0018468261 0.9897213949 0.0746386673 0.3141471169 0.1166915432 0.7870640083 0.8220060072 0.0127608223 0.2210547429 0.1746619989 0.0855102164 0.25 3 0 1
6 6.6584581771 0.6652518979 0.8598879317 0.6670564103 0.6171263508 0.9265904492 0.667359731 0.7693318951 0.1383282243 0.6913111195 0.2593602356 0.1358795941 0.2609743376 0.3 3.6 1 3
7 6.1280454065 0.9819240781 0.4579232303 0.8484705611 0.5556447088 0.1946123999 0.3431941944 0.228630832 0.3683624417 0.578508837 0.3483561749 0.990987977 0.2314299713 0.35 4.2 4 9
8 5.5754348406 0.9605296481 0.0994885439 0.3421793528 0.7045283755 0.2941132198 0.7014679577 0.0342064511 0.3968465247 0.5848745882 0.2077125019 0.7780039304 0.4714837465 0.4 4.8 13 19
9 6.6840812945 0.4757712548 0.2354913177 0.4353392557 0.7194283219 0.4310535494 0.5856354599 0.8128071591 0.9536298398 0.4382445644 0.1135209986 0.7464921204 0.7366674529 0.45 5.4 32 19
10 7.1138300152 0.559490067 0.684032548 0.8057255463 0.2404034157 0.1361362939 0.2139238071 0.7539943398 0.7437493927 0.601470717 0.4837721805 0.89312277 0.9980089372 0.5 6 51 16
11 6.3706705151 0.1397527782 0.2964798981 0.4585647854 0.6702165454 0.4420039108 0.6381412336 0.9385304054 0.2656635308 0.5463091932 0.6440865404 0.4295300352 0.9013916588 0.55 6.6 67 19
12 3.4010303112 0.2067073547 0.4408437801 0.7385417279 0.2466863222 0.1022945441 0.1774271763 0.0120350168 0.3787076839 0.3795802346 0.0555884759 0.6036724856 0.0589455088 0.6 7.2 86 10
13 5.2899844457 0.1213321502 0.0378987894 0.2882988268 0.4735759935 0.8677734286 0.5396755543 0.9226818992 0.4159332066 0.5490110169 0.7522510772 0.0671389977 0.2544135052 0.65 7.8 96 4
14 6.4841611716 0.711336647 0.0906114684 0.1497612914 0.9332861449 0.2138701478 0.5792426692 0.4489351725 0.3922209433 0.6345771118 0.8062143361 0.5528324779 0.9712727613 0.7 8.4 100 0
15 5.7848455809 0.1164942534 0.785254279 0.6973750974 0.4815499132 0.1700777969 0.5440791097 0.0556079578 0.7167932423 0.8002203266 0.5239597138 0.7714387669 0.1219951239 0.75 9 100 0
16 5.0443067154 0.2609179618 0.8687654202 0.0489908239 0.4506399783 0.7579073586 0.4920671579 0.1563690197 0.7240979702 0.2320040215 0.3595320716 0.1424526503 0.5505622813 0.8 9.6 100 0
17 5.9778238062 0.3356283633 0.9910983727 0.0330245284 0.3228450456 0.2510187778 0.6346036969 0.193417173 0.3437677679 0.5908114724 0.9645737321 0.7977052894 0.5193295868 0.85 10.2 100 0
18 7.6868349508 0.537078511 0.0273538608 0.1443650305 0.9509858063 0.5470019769 0.6755597941 0.9117011988 0.6094551485 0.9778315079 0.6555208157 0.743145364 0.9068359364 0.9 10.8 100 0
19 5.4569795807 0.269169932 0.6623962172 0.5099998625 0.9325470919 0.0965698703 0.4613545784 0.689481664 0.1054809254 0.4171267549 0.1439223785 0.61926084 0.5496694657 0.95 11.4 100 0
20 8.0114771321 0.2883598506 0.4350730932 0.8652332752 0.5386882048 0.7448797327 0.8272153425 0.6488287796 0.4388761831 0.7600836435 0.8549316294 0.7250343341 0.8842730634 1 12 100
21 6.5813843724 0.1473357101 0.8875466457 0.4189092146 0.8381537015 0.4824851118 0.6309012969 0.0103482582 0.5901564681 0.9615783806 0.0656822409 0.569659458 0.978627886
22 6.721049116 0.1227615461 0.0730901506 0.9771108519 0.8131777985 0.3640351326 0.830176126 0.7887062471 0.5159863796 0.947862973 0.6231575565 0.3242135318 0.3407708225
23 5.5537581259 0.2746387253 0.224729803 0.1497025199 0.7932090213 0.8166211798 0.46945034 0.3175800474 0.625617038 0.8902660547 0.3541274367 0.3734336876 0.264382272
24 6.6588866761 0.8072557296 0.8084710784 0.0638177669 0.8716187036 0.705838981 0.8400732867 0.166963511 0.8307394431 0.2332447614 0.2163080034 0.4477968477 0.6667585634
25 5.5965694576 0.8246041514 0.2729246323 0.6279799009 0.6281291537 0.7272208154 0.1523869755 0.397733246 0.3564835564 0.7992767663 0.2649057006 0.2738252975 0.2710992615
26 6.3462519634 0.8410201562 0.2667608864 0.8995936853 0.0165623544 0.5077414758 0.9457553557 0.2954927284 0.2959183385 0.8505331909 0.366298324 0.1912879118 0.869287556
27 5.2478363155 0.0613951413 0.0643102534 0.4867594579 0.8755853193 0.5122401093 0.0731560624 0.6510591667 0.2352331642 0.1906975727 0.7390765102 0.4945095777 0.8638139804
28 6.30771465 0.9871641229 0.1898956962 0.8103916935 0.9551218999 0.6475959 0.5215192368 0.3228135065 0.3761405889 0.1353683375 0.2391259247 0.3511962132 0.7713815301
29 5.9669129719 0.1981476489 0.7901714939 0.9022696967 0.0484939356 0.8325776796 0.667983893 0.0972473396 0.9463310069 0.0649833497 0.8525928125 0.2304852519 0.3356288638
30 5.0908776231 0.1050023472 0.9295154157 0.3812413152 0.7799915143 0.6943149954 0.0062167134 0.3424621341 0.7471958847 0.0246377321 0.1469415304 0.3889633402 0.5443947002
31 6.844834936 0.5250358519 0.5449938371 0.4963258215 0.4811133108 0.4197680656 0.6903010428 0.6766043288 0.8567447251 0.9271555152 0.0739043762 0.2595747292 0.8933133316
32 5.7036915007 0.8717308885 0.081428583 0.3919671281 0.7408465651 0.0277014905 0.8426605461 0.5841014506 0.4605793631 0.5638216415 0.2202610894 0.9060872775 0.0125054773
33 6.715634494 0.1952383567 0.2596011832 0.7205823797 0.3159184605 0.9969200316 0.2962005257 0.4893625778 0.329118099 0.9598602467 0.4927159692 0.742187954 0.91792871
34 7.8321096252 0.913554955 0.8236405333 0.4163187265 0.1324762936 0.4027609876 0.5409892956 0.9363723537 0.8826477899 0.9767479844 0.2672499583 0.5860830072 0.95326774
35 6.3958371717 0.8997843407 0.2303552061 0.4988212313 0.4538662735 0.9427093769 0.5663415785 0.8991555974 0.0415417805 0.0325520814 0.2950627601 0.6313624756 0.9042844697
36 4.524385233 0.4747932442 0.1285697656 0.4947107745 0.0050877454 0.3122749816 0.1027979259 0.8000705829 0.8580602464 0.4084007226 0.4990570233 0.3220612865 0.1185009341
37 5.5971268848 0.5255186825 0.6087401591 0.1183725164 0.1057381578 0.0266390426 0.984016146 0.7656538815 0.5424083532 0.8068604929 0.6927265325 0.2900952297 0.1303576907
38 5.3430358134 0.3500329352 0.9784142639 0.5379720978 0.072166401 0.527800616 0.3460529391 0.118026957 0.8133357534 0.2580684453 0.8453142184 0.3221680531 0.1736831333
39 5.6838488447 0.4411022286 0.5910587181 0.329553002 0.2499341562 0.4075254021 0.3328058174 0.1030080504 0.6724285507 0.9804910135 0.9740157012 0.3335424902 0.2683837143
40 6.9632967009 0.9025069197 0.1417537015 0.9533442793 0.4721861598 0.6886029345 0.3719183632 0.9503252506 0.1370847522 0.4291333191 0.1322924293 0.8880310341 0.8961175575
41 4.742583685 0.1608379707 0.5175740007 0.4696862833 0.016616026 0.8463690232 0.9959838285 0.0891905102 0.5251852128 0.6895339593 0.0145114821 0.1963095989 0.2207857893
42 5.5416204974 0.1386559382 0.1239630498 0.5956812667 0.4212875903 0.7915155349 0.8712956449 0.0642469293 0.1494215393 0.5498953293 0.4060782957 0.6991556202 0.7304237587
43 6.3706687861 0.5988888614 0.2840756601 0.8805788592 0.3535505859 0.3716217574 0.5342830176 0.3948223125 0.8246562306 0.9464271464 0.7601856282 0.2504715434 0.1711071833
44 6.315271985 0.8413385896 0.0324854196 0.4607473762 0.8761559842 0.5743277245 0.1338900333 0.4748842307 0.4606765309 0.0360161948 0.4810457213 0.9577236951 0.9859804848
45 7.936745272 0.7549014236 0.9824447491 0.518274464 0.9097344171 0.3340649641 0.7612582753 0.6907615051 0.2419853738 0.7162707193 0.8017800619 0.8791734868 0.3460958317
46 5.4792967234 0.1574427107 0.2301925819 0.4069975249 0.4187049842 0.9108456412 0.3542693498 0.5664445292 0.150182822 0.7876899797 0.3651097707 0.8700281926 0.2613886366
47 7.1401244416 0.0287554253 0.7411131588 0.3946653345 0.924061313 0.9344174196 0.9854681729 0.6735168223 0.0804889269 0.9378477086 0.1890499481 0.6381222766 0.6126179349
48 4.5656198015 0.3235534222 0.1398520328 0.9586370343 0.4050209526 0.1654674715 0.9276045049 0.2145669352 0.3102762786 0.177641631 0.4536935336 0.4211543839 0.0681516209
49 5.3119832358 0.6031732463 0.4751328903 0.0077662336 0.8668047521 0.7034696338 0.241603308 0.8346211384 0.2425310536 0.5146566838 0.110179497 0.1400375211 0.5720072778
50 4.7316053767 0.0120559397 0.1721963131 0.5027762919 0.3895495756 0.3531483881 0.0246057104 0.8317624707 0.3950590195 0.9960099634 0.547958241 0.0266644308 0.4798190327
51 4.6094262844 0.853859165 0.4069919946 0.114224143 0.4992462078 0.7555046824 0.0402358664 0.8106629039 0.0951939835 0.0230554055 0.4693375604 0.4584217401 0.0826926318
52 7.4515846077 0.853113276 0.558470703 0.9447651401 0.4109046245 0.892363483 0.009120074 0.6665310394 0.8903548434 0.9804108521 0.0422614895 0.6760870686 0.527202014
53 6.5433189478 0.9947503941 0.9316823857 0.2703896025 0.1026108517 0.2709369169 0.8868745473 0.335896647 0.9817234433 0.8723271067 0.1549459305 0.6928651748 0.0483159473
54 5.2553823893 0.638999082 0.6981704421 0.0375382538 0.5452045117 0.788551653 0.2290548974 0.1414049456 0.5690618732 0.3756496494 0.2994318778 0.1609109861 0.771404217
55 6.5465092486 0.0541457904 0.1084245006 0.9816612283 0.8729954144 0.9524460452 0.3174828446 0.3409588374 0.784840563 0.5473773184 0.5520948433 0.0731430668 0.9609387961
56 5.3158457776 0.38600884 0.9900890351 0.6257529411 0.3249695585 0.2450245277 0.8232907812 0.0676235513 0.5393947837 0.0749798323 0.8451452137 0.2623032507 0.1312634624
57 6.0104891933 0.1887881402 0.6650328115 0.7100524602 0.2669096078 0.099408966 0.417628104 0.8184851048 0.5514870898 0.1338693487 0.5722133956 0.9460456856 0.6405684792
58 4.1112848261 0.3346808452 0.534489615 0.3811690423 0.0134334385 0.4008801458 0.2255780755 0.0665020848 0.4065671192 0.9237721038 0.2442415633 0.3901490388 0.1898217541
59 5.0607562657 0.0814494848 0.6261857674 0.5371501331 0.1669237125 0.485243656 0.6101802006 0.8540417495 0.2758420853 0.9691047554 0.2156936015 0.0083189311 0.2306221885
60 4.6138733407 0.2695479336 0.4212125455 0.1216332492 0.0482636535 0.2220508031 0.2894244536 0.7141006613 0.152319946 0.5958829274 0.8879065721 0.4361974628 0.4553331325
61 6.6932169111 0.4074105814 0.815158511 0.0434949354 0.8424119184 0.9615007198 0.3420415302 0.8985583329 0.6555856881 0.5294687008 0.7902761824 0.1709915158 0.2363182949
62 7.0990248306 0.7379744237 0.0859183075 0.9397717581 0.8797059824 0.5685429086 0.8822153975 0.0763535762 0.848107838 0.0833018341 0.8113178873 0.5706011206 0.6152137967
63 6.1919545013 0.9166892862 0.3539589219 0.5870801046 0.7176709742 0.1705186384 0.8671703333 0.4934233268 0.0870473499 0.4210402219 0.8312682675 0.5642496665 0.1818374102
64 4.8698041497 0.1841714549 0.3067319204 0.2170057376 0.5682596484 0.9766029126 0.3457387543 0.1593959216 0.1349752957 0.5408586356 0.2657504634 0.9881205076 0.1821928974
65 4.8953543305 0.2639186578 0.2056201277 0.9135799909 0.433658367 0.7860894054 0.0111847813 0.646399206 0.3088205802 0.4207364024 0.0993107993 0.6990066428 0.1070293698
66 6.6350886252 0.5958947102 0.8384967447 0.0384036274 0.4104954321 0.4575743388 0.176212529 0.9702247274 0.9162907693 0.0584738057 0.995299351 0.8739069676 0.303815622
67 4.9128210155 0.3657305793 0.1094020493 0.1391920784 0.9089568917 0.6769841928 0.014623194 0.1075883961 0.8913471937 0.4570725195 0.2610037965 0.4385433208 0.5423768034
68 3.8455795357 0.553893589 0.0512982123 0.2018124411 0.1332431729 0.5127722323 0.251224123 0.5058041404 0.0613348135 0.1672351174 0.3932045791 0.7206483606 0.293108754
69 8.3744014256 0.9131564968 0.2672408479 0.8906531543 0.8731733992 0.9362951188 0.3092717692 0.6055724275 0.3301682097 0.9553636406 0.9341554573 0.3613807629 0.9979701414
70 4.7351981524 0.0895189942 0.1996617237 0.5347573012 0.0492421039 0.2307277231 0.4416847741 0.7219120805 0.0986025939 0.8921597985 0.4491935124 0.2888227883 0.7389147586
71 5.7772486397 0.1637060213 0.080561392 0.4112759114 0.5669681344 0.4400762559 0.9527899829 0.0288238723 0.6453313484 0.1451361354 0.4796903864 0.9046449113 0.958244288
72 6.8040863918 0.5403150668 0.3181437481 0.6274723649 0.7731160496 0.8854415345 0.6806317075 0.4727937954 0.4686896777 0.3926411303 0.3068238189 0.9818707104 0.3561467879
73 5.8089588167 0.1898971408 0.130086487 0.9926913253 0.7425688631 0.6539552474 0.7620898415 0.0709185481 0.4924820929 0.0850346776 0.3894723308 0.464272575 0.8354896872
74 4.6729457707 0.2837111934 0.4353623574 0.1407287257 0.4116493259 0.3810203339 0.6875003731 0.1317730527 0.670183681 0.1272360413 0.5370673753 0.3978063835 0.4689069275
75 7.2529468129 0.7028218373 0.1052280675 0.7880209154 0.5953072505 0.9960174171 0.5160308057 0.694672433 0.2117339741 0.7963706531 0.3202235185 0.6691013145 0.8574186262
76 7.1653870818 0.9077797763 0.1575563696 0.7694239127 0.7066698887 0.5943811138 0.3005183058 0.6147123677 0.1998546529 0.7639652103 0.9994519235 0.1779243575 0.973149203
77 4.9889509126 0.5522121769 0.2195413194 0.113075964 0.2355604405 0.2200090654 0.8293337966 0.8121922668 0.4349929517 0.7425167505 0.0629167309 0.5948179754 0.1717814745
78 6.7569213264 0.6856765229 0.2493967113 0.3474203606 0.5617514734 0.5425830646 0.9756830082 0.2657959727 0.4792157829 0.575070441 0.9862544873 0.6997392598 0.3883342419
79 5.2841426475 0.394089549 0.5589990516 0.5315593182 0.2128260364 0.3242504942 0.9267198992 0.5180518386 0.2100526813 0.2532429529 0.4334073785 0.1346649143 0.7862785333
80 6.9105261487 0.4086647371 0.6001097324 0.8322203988 0.4228419127 0.4827803235 0.8362353237 0.4569889757 0.9292153957 0.2364581623 0.6072084965 0.5676521973 0.530150493
81 5.8487668466 0.4956247987 0.7696781146 0.7705819372 0.1951399004 0.2248874156 0.7809938565 0.9254380503 0.147575915 0.3048195667 0.1102071251 0.8842706611 0.2395495054
82 5.3720041609 0.8946962586 0.0227276432 0.7467135004 0.0995124777 0.4408514246 0.4140741852 0.3945438497 0.5595321065 0.0749931406 0.6400701227 0.7779792998 0.3063101519
83 4.9169099424 0.127582981 0.5294391672 0.6357840531 0.5345094513 0.1587689685 0.4257856824 0.0805846614 0.6279501182 0.586613579 0.1893353598 0.7351892669 0.2853666534
84 6.7269156884 0.9754724392 0.2051078672 0.288521827 0.0979548508 0.3866086492 0.211506308 0.6552711272 0.9505011305 0.7122386992 0.5597673919 0.9252137091 0.758751689
85 7.2332223845 0.9373889901 0.4119795136 0.7559459244 0.0328005792 0.710840432 0.6895765314 0.080791493 0.5586862751 0.5229840031 0.8068807979 0.7421530613 0.9831947835
86 6.1284284762 0.5236748592 0.2891501431 0.9322425387 0.6044668007 0.887338961 0.0840910126 0.0815475644 0.4486807846 0.328931023 0.9376639574 0.7121943508 0.2984464809
87 7.784399564 0.6478745113 0.1968043617 0.8871034928 0.8335544414 0.9594340297 0.5945215323 0.338101294 0.7395104135 0.4682596924 0.8040655889 0.8145399396 0.5006302662
88 4.5132502343 0.1384763368 0.3843588933 0.1669652893 0.0895126443 0.124809737 0.8972018693 0.6958393561 0.8156329033 0.0688455575 0.5455407759 0.0122341342 0.5738327374
89 7.7832875143 0.5747464451 0.5348365637 0.2226415296 0.8355690648 0.3646150374 0.90279783 0.7888959906 0.6291672347 0.8299548689 0.8431525561 0.3609219722 0.8959884211
90 7.2706147289 0.4900963589 0.5529430327 0.6578605636 0.5298474434 0.5896253718 0.7503738194 0.4559046288 0.6142882415 0.7839105469 0.8893423643 0.3729744034 0.5834479543
91 6.9582172008 0.5253219275 0.6180977182 0.8998711034 0.3673928785 0.9249237782 0.4634125096 0.4638501172 0.5020210748 0.8345700789 0.6973694464 0.3489582501 0.312428318
92 5.0621910229 0.3971376976 0.5797812941 0.0746277962 0.1654417415 0.3747112942 0.4842006123 0.5910708741 0.3297968442 0.6375637131 0.3730426934 0.5142288879 0.5405875742
93 6.4115949215 0.2835859189 0.5979960163 0.5584246822 0.1627140236 0.7949712033 0.7910559804 0.71976123 0.8384258798 0.4799787942 0.7561239714 0.3129099244 0.115647297
94 5.4582602784 0.9290474035 0.69180805 0.2193178777 0.2958268807 0.9578746503 0.2823171764 0.0613343084 0.2533330685 0.5221554925 0.2770422805 0.5324564595 0.4357466306
95 5.8568894255 0.9914838459 0.0026189529 0.4165221796 0.3281398582 0.2995756916 0.3931309509 0.5054011005 0.4000762995 0.9228210555 0.9449330154 0.3299250024 0.3222614729
96 5.9621227798 0.7967383398 0.6080741839 0.6205097497 0.8613606918 0.0469330721 0.4439615057 0.7511311267 0.2171627666 0.1038460399 0.5320318533 0.7724838092 0.2078896411
97 5.6901709891 0.5405629429 0.1935571045 0.3764943556 0.9437656019 0.1475067757 0.6231742011 0.9167998647 0.1465446503 0.8588972073 0.2383587862 0.1469820044 0.5575274945
98 7.5452019042 0.9136690334 0.2953624118 0.902342111 0.1038239128 0.7619272691 0.6924033676 0.6099230019 0.8067240598 0.4761094872 0.2376035562 0.7788927088 0.9664209845
99 5.0834554466 0.2082907394 0.1421642979 0.5245472059 0.9259669251 0.634702567 0.1657954515 0.2870383582 0.5340734479 0.0825007103 0.628126404 0.7735017739 0.1767475656
100 4.9057130609 0.3894880331 0.2593091364 0.6247611718 0.3370605564 0.8789577398 0.2199440971 0.6286168226 0.5905009017 0.5404249763 0.2941327136 0.0674952634 0.0750216486
0.0 0.0 0.0 0.0 0.0 1.0 3.0 9.0 19.0 19.0 16.0 19.0 10.0 4.0 0.0 0.0 0.0 0.0 0.0 0.0

DataTable1D

Set F to the number of random draws that you with to sum together.
You can observe the distribution that emerges on the right.
At F=1, you see that values are just uniformly distributed.
At F=12, you can clearly see the normal distribution emerge out of randomness.
F
12
F_Row 1 2 3 4 5 6 7 8 9 10 11 12 Bins CDF PDF
n 6.5965267558 0 0 0 0
1 5.1938383385 0.0424592398 0.1437695683 0.9707747131 0.616295432 0.7168689743 0.7861467979 0.2277155869 0.9477114235 0.8338688704 0.5552236806 0.0887719027 0.6669205664 0.05 0.6 0 0
2 6.9854852857 0.1 1.2 0 0
3 6.5612347921 0.15 1.8 0 0
4 5.6519843139 0.2 2.4 0 0
5 5.8931081159 0.25 3 0 0
6 4.9716982338 0.3 3.6 0 2
7 5.9210807087 0.35 4.2 2 12
8 4.7400603805 0.4 4.8 14 24
9 6.0413021487 0.45 5.4 38 23
10 5.0492501579 0.5 6 61 18
11 6.4906987927 0.55 6.6 79 12
12 7.1183838325 0.6 7.2 91 6
13 6.1049368356 0.65 7.8 97 3
14 4.2881039119 0.7 8.4 100 0
15 5.0155271631 0.75 9 100 0
16 6.0905272102 0.8 9.6 100 0
17 7.3257666133 0.85 10.2 100 0
18 4.8571403487 0.9 10.8 100 0
19 6.7358004212 0.95 11.4 100 0
20 7.0647668097 1 12 100
21 7.2336911753
22 5.1568158452
23 5.0638031778
24 4.700613536
25 7.1997068741
26 5.8313086044
27 5.6461674691
28 5.5849020973
29 4.6625617202
30 5.6256813159
31 5.6657690847
32 6.0888706784
33 5.0405759152
34 4.8746679375
35 6.1679483196
36 6.7194683111
37 5.7203003037
38 6.2378622701
39 5.255744246
40 5.2606235432
41 7.5780313472
42 6.2235130943
43 7.1801780831
44 4.7477112207
45 5.5710169669
46 4.9948212335
47 5.9461671394
48 6.0259580167
49 6.5588521034
50 4.4490297009
51 8.3550839878
52 5.7481509067
53 5.2985169034
54 4.5848678038
55 5.3547326242
56 5.0983489169
57 5.5829227508
58 5.8735815179
59 5.6995377621
60 5.2830652859
61 5.3222678941
62 6.4406560726
63 5.4360561899
64 4.4108576321
65 5.6049375662
66 7.8442790459
67 6.6633598619
68 6.4162873154
69 6.0533811156
70 7.3767416116
71 4.16062442
72 6.4595088706
73 5.4556098914
74 6.823373064
75 7.2656578882
76 5.1543039153
77 5.4075521642
78 6.5201596798
79 4.7814240128
80 6.7536239274
81 4.1983088453
82 5.2403473805
83 7.8446616825
84 6.2163804039
85 5.1244780487
86 6.251830848
87 5.4511785922
88 4.8489774192
89 4.6431482902
90 5.1725380462
91 5.878623735
92 4.837793409
93 5.5870409208
94 4.8400056731
95 7.1161430882
96 7.2209270364
97 5.7489123717
98 6.657856671
99 4.742338969
100 4.7249684927
0.0 0.0 0.0 0.0 0.0 0.0 2.0 12.0 24.0 23.0 18.0 12.0 6.0 3.0 0.0 0.0 0.0 0.0 0.0 0.0

FindMuSigma

Mu 300
Sigma 100
Likelihood -7526.0947375881
mu 100 300
sigma 5 100
p(Data1) Data1 DataTest
0.0004974637 1 95.9471026793 239.1912645756 -5 75 0 0 75 0 0 0
0.0005444857 2 100.4224408589 170.0259416762 -4.5 77.5 0 0 77.5 0 50 20
0.0004911132 3 95.3184320073 183.7262726019 -4 80 0 0 80 0 100 40
0.0007347491 4 116.0503969757 405.0022534431 -3.5 82.5 0 0 82.5 0 150 60
0.0005305736 5 99.1297348168 392.574265953 -3 85 5 5 85 5 200 80
0.0005730935 6 103.0049282076 368.2520981672 -2.5 87.5 12 7 87.5 7 250 100
0.0006014524 7 105.4721399309 305.1193176274 -2 90 21 9 90 9 300 120
0.0004860804 8 94.8158018865 424.777035561 -1.5 92.5 56 35 92.5 35 350 140
0.0006060212 9 105.8615470318 362.3779994622 -1 95 157 101 95 101 400 160
0.0005209182 10 98.2175013529 158.170997143 -0.5 97.5 318 161 97.5 161 450 180
0.0005728859 11 102.9865343528 212.043623128 0 100 514 196 100 196 500 200
0.0006234292 12 107.3258379183 236.3412674279 0.5 102.5 704 190 102.5 190
0.0005231041 13 98.4251322983 541.0069860735 1 105 843 139 105 139
0.0005164959 14 97.7954247743 79.1774408516 1.5 107.5 927 84 107.5 84
0.0005118587 15 97.3498945318 182.3520598505 2 110 974 47 110 47
0.0006045099 16 105.7329811635 386.5314462703 2.5 112.5 993 19 112.5 19
0.0005139662 17 97.5527601918 284.3403879252 3 115 998 5 115 5
0.0005563766 18 101.5078656861 191.099107942 3.5 117.5 1000 2 117.5 2
0.0006280846 19 107.7123551982 253.0408000978 4 120 1000 0 120 0
0.0005239144 20 98.5019379672 364.6236661479 4.5 122.5 1000 0 122.5 0
0.0004847602 21 94.6832896991 417.3950685997 5 125 1000 0 125 0
0.0004752241 22 93.7178978443 501.1381238676 -5 -200 0 0 -200 0
0.0006288339 23 107.774367772 67.6690128481 -4.5 -150 0 0 -150 0
0.0006335288 24 108.1617122405 247.6901562516 -4 -100 0 0 -100 0
0.0005746063 25 103.1387913876 336.304070098 -3.5 -50 1 1 -50 1
0.0005217132 26 98.2930877872 313.8844570074 -3 0 2 1 0 1
0.0005011678 27 96.3109753955 166.6067716579 -2.5 50 6 4 50 4
0.0005118389 28 97.3479913453 352.5890648802 -2 100 21 15 100 15
0.0005720851 29 102.9155483653 297.8531820666 -1.5 150 55 34 150 34
0.0005216723 30 98.2892013184 324.2204246707 -1 200 149 94 200 94
0.0004943576 31 95.6403791837 358.3965767231 -0.5 250 283 134 250 134
0.0004826012 32 94.466003387 224.5261348032 0 300 485 202 300 202
0.0004939445 33 95.5994815907 319.3462996603 0.5 350 676 191 350 191
0.0004972094 34 95.9220481498 405.7720674242 1 400 836 160 400 160
0.0006064814 35 105.9006538359 342.9125965416 1.5 450 931 95 450 95
0.0005453915 36 100.5057441634 85.6291355634 2 500 979 48 500 48
0.0005356202 37 99.6015695075 258.6789721805 2.5 550 997 18 550 18
0.0004734764 38 93.539365366 379.3224267278 3 600 1000 3 600 3
0.000517658 39 97.906607797 180.0012968444 3.5 650 1000 0 650 0
0.0006529814 40 109.744736814 470.0745301548 4 700 1000 0 700 0
0.0005394457 41 99.9570203114 275.2502563939 4.5 750 1000 0 750 0
0.0006247506 42 107.4357569686 229.0726892452 5 800 1000 0 800 0
0.0005913919 43 104.606911698 198.3676542333
0.0004651053 44 92.6771554071 425.6287071552
0.0004889787 45 95.1057344917 121.3499870827
0.0005185413 46 97.9909809852 191.9046431594
0.0005686779 47 102.6126789849 260.55177467
0.0005890461 48 104.4036121786 202.9788718104
0.0007165363 49 114.690911209 159.266795477
0.0005902341 50 104.506640651 205.6420271864
0.0005251309 51 98.6170636673 197.6225503708
0.000523032 52 98.4182926727 448.3966224226
0.0005010399 53 96.2984468608 191.7780621389
0.0006355357 54 108.3266508207 348.1208127542
0.000547301 55 100.6810129858 463.3215688521
0.0005637892 56 102.1757640304 358.9126463716
0.0005344449 57 99.4919889756 171.3151079652
0.0005095955 58 97.1313462898 462.4657844845
0.0004691801 59 93.0983237405 432.8692103204
0.0005520439 60 101.1143919911 293.4820931981
0.0005198299 61 98.113887736 309.8585274067
0.0005411707 62 100.1166791177 216.2001154192
0.0005018907 63 96.3817601161 244.9020176835
0.0004719635 64 93.3844013972 432.8881999942
0.0005342685 65 99.4755240783 418.1005503742
0.0005463914 66 100.5975837823 252.9859047177
0.0005156573 67 97.7150760849 401.3218612288
0.0006177851 68 106.8543993969 440.4509214599
0.0005956147 69 104.9713945661 399.9730249175
0.0005766083 70 103.3155490255 416.0169873279
0.0005652537 71 102.3069458115 397.4783183566
0.0005147824 72 97.6311532325 414.9493436433
0.0004889112 73 95.0989968726 126.4587073168
0.000515993 74 97.7472548022 316.9491469117
0.0005910493 75 104.5772559817 275.7602362693
0.000565804 76 102.3561692765 358.577702043
0.0005510062 77 101.0198111087 418.4834129577
0.0004660303 78 92.7730123529 332.9967423758
0.0005273517 79 98.8267372795 121.119506393
0.0005269489 80 98.7887575826 261.3908140757
0.0005209797 81 98.2233503512 379.3315838526
0.0005144908 82 97.603155386 349.9332174737
0.0004848868 83 94.6960101338 319.3533973611
0.0005079007 84 96.9672033518 308.5990119813
0.0005816018 85 103.7544513288 267.0150562892
0.0005369624 86 99.7264985429 433.8659964211
0.0006147535 87 106.5998702498 206.8797810908
0.0005490445 88 100.8406498869 245.4604890041
0.000513633 89 97.5207273748 150.642050241
0.0005436013 90 100.3410024329 290.1943285836
0.0004730152 91 93.4921627141 251.4881147995
0.0005254535 92 98.6475650294 391.3214424606
0.0005304264 93 99.1159225416 307.0624217824
0.0005381768 94 99.8393260462 228.023712471
0.0006295753 95 107.8356740517 278.4154556952
0.0006002174 96 105.366499869 188.7455585147
0.0005001022 97 96.2065112081 314.2292653854
0.0004779725 98 93.9976346544 349.304329222
0.0004924191 99 95.4482144045 397.7584812828
0.0005400491 100 100.0129075365 509.2410198517
0.000421019 101 87.9281271817 456.2144708134
0.0005469104 102 100.6451980342 393.6234567756
0.0005416665 103 100.1625000676 129.4008264302
0.0005196533 104 98.0970506151 208.682844489
0.0004438688 105 90.4350759958 430.5960686291
0.0006457118 106 109.1572100259 417.9996925656
0.0005220152 107 98.321786265 216.2385691189
0.0005728225 108 102.9809169634 262.0833198654
0.0005876831 109 104.2852065607 355.6033854923
0.0006150411 110 106.6240616424 274.8353187717
0.0004973608 111 95.9369653067 212.1303708914
0.0004754018 112 93.7360178427 238.9261889525
0.0005397596 113 99.9861027385 242.4995746292
0.0005346682 114 99.5128186023 536.0565059105
0.0005316636 115 99.2319319004 14.92686399
0.0005466771 116 100.623797679 383.3393780004
0.0005246338 117 98.5700428752 203.8748620884
0.0005250435 118 98.6087984964 395.9650044712
0.0005622141 119 102.0343937467 358.3757019093
0.000479327 120 94.1350529493 342.951205404
0.0005563184 121 101.5025936671 195.5636793891
0.0005601457 122 101.8482905939 427.7262957222
0.0005501092 123 100.9379454992 294.6022006393
0.0005485536 124 100.7957442881 383.0068241837
0.0004941795 125 95.6227483764 348.9304017026
0.0005163276 126 97.7793073973 359.2701313447
0.0005116496 127 97.3297311476 307.8378775516
0.0005259333 128 98.69289741 388.4411777494
0.0006503812 129 109.5351374453 118.4368739932
0.0005876278 130 104.2804004954 324.7329396631
0.0005106896 131 97.2370925983 319.9586799832
0.0005642114 132 102.2136057802 292.8390996142
0.0005591377 133 101.7574152989 456.7635457687
0.0005603899 134 101.8702970731 441.6006264052
0.00062026 135 107.0615088174 51.9597355061
0.0005537187 136 101.2667635479 304.4294557191
0.0004137745 137 87.1112617163 308.007561152
0.0006173538 138 106.8182448639 274.4503194245
0.0005141724 139 97.5725704798 365.0736496265
0.0005620893 140 102.0231813814 102.9415866646
0.0004987218 141 96.0709220767 426.4662133899
0.0004684377 142 93.0217972162 280.8663033804
0.0006314709 143 107.9921851699 278.0752182741
0.0005300042 144 99.0762921084 321.3285947262
0.0005665736 145 102.424960036 378.2977220943
0.0005913222 146 104.600881773 358.6034398705
0.0004865919 147 94.8670598597 316.7489065182
0.0005597071 148 101.8087686519 427.7697048987
0.0005134211 149 97.5003455014 252.8726239371
0.0006557671 150 109.9686281565 338.3849759577
0.0005350727 151 99.5505453064 442.5756509351
0.0005208752 152 98.2134142008 328.4573254509
0.0005235535 153 98.4677382156 215.8425603069
0.0005333971 154 99.3941332787 46.2806318001
0.0005774827 155 103.3926048858 462.4251976485
0.0005092066 156 97.0937124799 155.2305987024
0.0006097588 157 106.1785171951 81.1421545293
0.0005209425 158 98.2198131745 247.018911239
0.0004222597 159 88.0669284076 303.6836190935
0.0004991374 160 96.1117767775 440.6812129842
0.0005913532 161 104.6035666792 421.1530212675
0.0004925561 162 95.4618120462 257.1733050289
0.0005471086 163 100.6633726922 322.2539294731
0.0004715573 164 93.3427384225 233.1683539066
0.0005345831 165 99.5048779316 282.8920598539
0.0005366492 166 99.6973646849 280.9203689413
0.0005754347 167 103.2119873911 216.8637324186
0.0006280019 168 107.7055086681 313.2187316619
0.0004560069 169 91.7264367172 160.3044108094
0.0005848237 170 104.0361577902 290.4816102703
0.0003817656 171 83.3622813639 220.3933343373
0.0006090753 172 106.1206630539 322.5630557449
0.0006132562 173 106.4738239556 333.8293138989
0.0005617016 174 101.9883308013 244.4298381278
0.0005234673 175 98.4595680469 386.0307042577
0.0005267512 176 98.7701082718 223.6346236791
0.0005846148 177 104.0179249758 317.3216813333
0.0005866199 178 104.1927069548 214.8435537455
0.0004571643 179 91.8481780786 430.661007064
0.0005482428 180 100.7672910925 389.2737834872
0.0005921303 181 104.6707828515 267.8033469875
0.000457699 182 91.9043498712 258.9310323689
0.0004971165 183 95.9128934265 191.0993419995
0.0005904026 184 104.5212483713 391.8913087012
0.0004683399 185 93.0117130683 181.1554924175
0.0006725654 186 111.3043462599 285.9577827459
0.000579548 187 103.5742744218 459.5495518458
0.0005917907 188 104.6414165009 273.6891071035
0.0005554713 189 101.4258357632 352.9299579381
0.0004834435 190 94.5508593626 303.8387388563
0.0005059267 191 96.775494221 270.3283474764
0.0006269617 192 107.6193163673 470.8739197676
0.0006630154 193 110.5479686507 266.8103485683
0.0005526648 194 101.1709201476 398.182084784
0.0004920504 195 95.4115966975 228.8234183388
0.0005511523 196 101.0331390705 446.1494219672
0.0005670782 197 102.4700206377 216.1931048949
0.0005472401 198 100.6754297718 247.9100607268
0.0005193388 199 98.0670747332 158.5884006478
0.0005485741 200 100.7976212579 266.5162699098
0.0005848211 201 104.0359318241 202.0652611445
0.0005313205 202 99.1997756892 30.2606174986
0.0005509042 203 101.0105057454 449.7216290229
0.0005390567 204 99.9209640772 250.8877731647
0.0004671455 205 92.888382783 448.4308403841
0.0005639025 206 102.1859235499 171.6204679859
0.0004853438 207 94.7419057969 557.7133403663
0.0004739518 208 93.5879781216 450.3782494446
0.0004825307 209 94.4588935032 311.2616234346
0.0005677526 210 102.5302022875 339.2590690954
0.0006545506 211 109.8709431888 234.2647993678
0.0005806092 212 103.6674261987 457.2629868183
0.0005821917 213 103.8061140241 394.7886160364
0.0005085699 214 97.0320652697 340.8049229294
0.0004865341 215 94.8612705655 229.0694576206
0.0006123367 216 106.396307761 320.159302867
0.0005634697 217 102.1471126102 572.5367399262
0.000581797 218 103.7715476844 309.0491090068
0.0005838296 219 103.9493605973 395.950183829
0.0006358257 220 108.3504552526 305.5548833241
0.0005359215 221 99.629635868 420.2349738418
0.0006537893 222 109.8097413357 223.3279302035
0.0005134998 223 97.5079172655 347.1658096025
0.000499634 224 96.1605500591 365.793040458
0.0005356361 225 99.6030530425 259.9679572458
0.0006120378 226 106.3710866698 278.732967598
0.0004978152 227 95.9817209116 330.8364992526
0.0005588425 228 101.7307805474 259.0061384679
0.0004727582 229 93.4658515716 357.0413252153
0.0005581318 230 101.6666083203 361.9722535495
0.0005072345 231 96.9025642976 173.445320837
0.0004690064 232 93.0804258801 150.11456882
0.0004809542 233 94.2997473877 361.4201324143
0.0004946833 234 95.6726127827 371.5528880609
0.0005644443 235 102.2344732312 315.5100748523
0.0005191681 236 98.0507959049 267.2945462358
0.0005699631 237 102.7270850734 299.0579511537
0.0005601574 238 101.8493531292 232.4609344357
0.0005210456 239 98.229619782 278.6943440504
0.0005862102 240 104.1570312245 310.127734575
0.0004798313 241 94.1861373315 181.9191368993
0.0006204149 242 107.0744474275 370.1260930574
0.0005064989 243 96.8311193524 266.9535490908
0.0005360124 244 99.6381002308 450.5115871992
0.0005434359 245 100.3257639572 451.6481692113
0.0005787331 246 103.5026537525 424.3596257622
0.0005928103 247 104.7295563232 451.9840693905
0.0005948179 248 104.902770057 338.9326514816
0.0006142972 249 106.5614792873 423.3735069798
0.0006145011 250 106.5786413311 366.0845152751
0.0004917959 251 95.3863107785 299.4919983451
0.0005391957 252 99.9338506133 349.0666533006
0.0004720886 253 93.3972372254 331.8654919416
0.0005378617 254 99.8100669452 237.6918637541
0.0005176991 255 97.9105289142 177.7123062261
0.0005427376 256 100.2613811515 188.1596134442
0.0004502487 257 91.1171700772 426.8951307777
0.0005827839 258 103.8579398581 318.4808821512
0.0005200183 259 98.1318339638 393.1918468975
0.0004944731 260 95.6518102572 362.1677199095
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DataTable

mu
0
sigma
1
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Surface

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__MACOSX/._Excel_DataTablesHistogramsDistributions.xlsx

LogNormal.xlsx

LogNormal

A lognormal random variable is a variable that is normal after you log it.
The log function is the inverse of the exponential function.
Ln(ex) = x
So if you exponentiate x, and x is normally distributed, you create a lognormal random variable.
n x ex
1 0.551955286 1.7366453386
2 -1.196444918 0.3022668876
3 1.1424535892 3.1344495898
4 -1.4060017881 0.2451213737
5 0.8833637199 2.4190229521
6 -1.8840324604 0.1519760311
7 -1.222726243 0.2944263939
8 -1.178628706 0.3077003971
9 -0.194787301 0.8230096928
10 1.463612253 4.3215418701

Sheet1

__MACOSX/._LogNormal.xlsx