================================
LATIHAN 1 – SIMULASI MONTE CARLO
================================
Soal:
Warung es teh mencatat permintaan selama 100 hari:
50 (10x), 60 (20x), 70 (40x), 80 (20x), 90 (10x)
1. Tentukan distribusi probabilitas
2. Prediksi permintaan 5 hari ke depan
3. Prediksi permintaan 20 hari ke depan
permintaan <- c(50, 60, 70, 80, 90)
frekuensi <- c(10, 20, 40, 20, 10)
prob <- frekuensi/sum(frekuensi)
# Simulasi 5 hari
set.seed(5)
sim_5 <- sample(permintaan, 5, replace = TRUE, prob = prob)
sim_5
## [1] 70 80 50 70 70
mean(sim_5)
## [1] 68
# Simulasi 20 hari
set.seed(20)
sim_20 <- sample(permintaan, 20, replace = TRUE, prob = prob)
sim_20
## [1] 90 80 70 60 50 50 70 70 70 70 80 80 70 80 70 60 70 70 70 90
mean(sim_20)
## [1] 71
expected_value <- sum(permintaan*prob)
expected_value
## [1] 70
==========================================
LATIHAN 2 – DISTRIBUSI EKSPONENSIAL & NORMAL
==========================================
Soal:
Bangkitkan data:
- Eksponensial (permintaan, 10 data)
- Normal (frekuensi)
Lalu prediksi permintaan:
5 hari, 20 hari, 100 hari, 1000 hari
set.seed (123)
permintaan_exp <- rexp(10, rate = 0.1)
frekuensi_norm <- rnorm(10, mean = 50, sd = 10)
permintaan_exp
## [1] 8.4345726 5.7661027 13.2905487 0.3157736 0.5621098 3.1650122
## [7] 3.1422729 1.4526680 27.2623646 0.2915345
frekuensi_norm
## [1] 45.54338 62.24082 53.59814 54.00771 51.10683 44.44159 67.86913 54.97850
## [9] 30.33383 57.01356
# simulasi
sim_5 <- rexp(5, rate = 0.1)
sim_20 <- rexp(20, rate = 0.1)
sim_100 <- rexp(100, rate = 0.1)
sim_1000<- rexp(1000, rate = 0.1)
sim_5
## [1] 9.658712 14.852758 13.480445 11.685290 16.058523
sim_20
## [1] 14.9674287 15.7065255 0.3176774 5.9784969 21.6783975 5.0661573
## [7] 2.5955782 25.9689212 12.2902573 7.9068176 6.2928008 12.5464100
## [13] 5.8868464 11.2929003 4.2036480 72.1100758 8.4572197 2.2554201
## [19] 11.0033882 22.4830569
sim_100
## [1] 13.63734299 5.76391668 27.25275850 13.12163043 0.90591350 3.06203850
## [7] 10.67213070 3.13516256 9.74640151 18.87823315 5.64588603 25.76961329
## [13] 10.47695748 10.24441342 10.27869616 2.84668461 15.63051889 0.42088293
## [19] 0.98630890 0.98569312 2.80385161 2.95786959 9.72429649 9.24027224
## [25] 16.42404527 16.19912768 25.36145540 15.21549623 3.80014203 2.38512967
## [31] 4.66487424 0.42271452 3.19676899 6.43610920 5.72563103 2.16055503
## [37] 44.98673398 18.57090553 6.85458638 14.39452626 17.31153984 12.44783300
## [43] 14.63300560 15.37393979 0.04599127 11.08765468 2.99970318 11.92003007
## [49] 11.14928704 0.67375891 4.80668721 15.70454339 2.59946107 18.56922287
## [55] 4.63219621 2.36035747 11.82099421 0.59671372 4.03238441 9.42939840
## [61] 4.16580644 7.53218405 1.88686388 8.76853871 1.90037821 9.79078206
## [67] 3.23375827 13.20477554 3.18460648 16.05067296 1.45734116 18.03129319
## [73] 0.30059454 13.03440549 1.99792245 17.51456242 17.63668332 8.43043578
## [79] 3.48752776 32.97824800 4.01706175 11.00701734 13.28923172 6.41902648
## [85] 1.95833715 4.56788857 3.72750164 34.63594891 12.74027719 10.81485151
## [91] 2.96959161 0.84160734 29.53400917 19.68252255 6.63855126 16.09392144
## [97] 6.06837084 0.93652313 3.24635284 17.59882312
sim_1000
## [1] 2.661107196 9.406261677 4.491086928 12.889064792 1.782890626
## [6] 15.717260875 0.621407977 5.705833426 17.307808454 13.107439046
## [11] 12.948729662 4.673107091 0.328897885 1.530380426 10.384720042
## [16] 10.824457062 37.472911382 0.056260913 0.043673706 16.999841611
## [21] 5.406681485 4.703686116 0.515594157 5.171863390 14.831430092
## [26] 12.794855590 14.264681739 21.182943414 14.241603741 8.841143110
## [31] 26.909868586 22.299070972 5.228044602 0.686505648 5.691505331
## [36] 43.659109359 5.581317656 4.587813038 2.602637056 6.988417450
## [41] 9.631883885 7.314795549 11.122795706 6.056245458 6.714176740
## [46] 16.316588301 1.019261316 4.079841226 27.403485532 28.518774582
## [51] 0.241733721 4.755948060 6.681086184 9.502303022 11.377750027
## [56] 0.827650866 16.429077049 1.589004147 14.786159377 1.130317389
## [61] 2.241256704 6.705106399 15.368307102 19.288219362 2.135722003
## [66] 5.678929575 19.333238005 36.027478629 13.195786457 9.307641349
## [71] 3.154568624 1.447820521 9.282945115 2.583424659 5.383878225
## [76] 0.753543661 1.284377063 25.988401527 20.701909940 2.053810175
## [81] 27.661254796 14.563427714 27.629222977 14.828341323 2.741042617
## [86] 7.503337262 10.503975013 3.615751024 9.609441729 6.631371961
## [91] 15.776374134 19.224809109 2.230031494 38.452058895 1.925270893
## [96] 9.808966834 2.099576880 12.459658356 16.700951009 3.906887232
## [101] 10.113368341 0.749836427 26.705747152 16.756204627 8.251186637
## [106] 1.677446719 4.634153177 17.104616500 4.911461654 15.629672296
## [111] 11.253750342 3.466649628 0.476452033 10.923543516 14.266298407
## [116] 5.181388311 16.255881674 21.940174406 1.698731147 7.762592583
## [121] 15.823527044 6.207961324 25.821072551 6.440601423 11.522778269
## [126] 6.934697359 15.354364058 6.278674426 9.242026778 3.754853713
## [131] 0.802523482 3.564477148 12.715098659 22.072651851 7.534095128
## [136] 0.343374270 5.738547053 11.075714845 11.589129604 8.415477033
## [141] 23.590081389 11.549642589 18.104048780 0.721074413 0.078974240
## [146] 2.365858856 23.999404478 2.742510571 17.602416090 7.365728503
## [151] 6.301629902 8.977172784 11.518312925 9.415983483 29.684275983
## [156] 0.376098468 3.580268314 0.176937591 9.046976789 3.098624326
## [161] 6.329562776 30.365630536 4.780633710 10.880251554 6.585016469
## [166] 0.710827834 7.913286350 6.018964238 25.457566584 6.642155484
## [171] 8.005674704 5.062201992 0.564683164 6.044764342 12.338415989
## [176] 10.035367766 20.258039850 1.387653253 3.671698290 3.314702851
## [181] 0.597849172 0.196857988 35.000066811 32.993082402 1.393784621
## [186] 3.005230008 3.075333647 12.741622263 6.246096571 0.940468353
## [191] 3.835280304 1.749227340 11.846148043 13.463688129 36.410372609
## [196] 1.334681655 12.565737294 11.647309716 1.048996268 3.334103157
## [201] 0.421310278 0.612487730 0.167412595 10.431271698 0.221610439
## [206] 3.729807022 15.068907532 6.028591674 15.565508249 6.454347833
## [211] 10.171384951 11.898247320 2.594908476 26.255814301 38.733336830
## [216] 4.047555645 5.097309072 0.306004157 5.508151827 12.004128480
## [221] 31.200462802 11.507915072 7.881522597 2.110479221 5.182706788
## [226] 6.896692486 7.652889937 19.075670625 6.379107665 13.642555875
## [231] 1.876769862 5.976471156 0.626064980 2.514872742 4.912724346
## [236] 24.454968589 8.952176254 2.291243146 5.058641159 3.297651217
## [241] 4.732406922 0.390811805 0.058166082 10.953262727 6.911122459
## [246] 6.128703277 22.425174873 22.787495608 1.089404349 17.744363303
## [251] 37.504724914 0.426276927 24.598878341 8.251565648 13.748867847
## [256] 1.745562484 6.133888592 20.022560320 10.037763164 4.295096211
## [261] 6.624439578 3.816584283 0.446715322 17.518804035 7.207210169
## [266] 2.696010196 0.791218281 15.071227606 8.279942879 1.660611904
## [271] 17.065014987 26.202593128 9.397423068 7.336770752 39.469834024
## [276] 2.319187020 0.928525175 11.989251533 18.732784818 10.541675878
## [281] 3.192426744 4.587218626 6.957008925 0.747814868 4.213419634
## [286] 4.247464860 39.284356439 13.608053792 4.487067587 17.640951294
## [291] 9.563983371 6.085125585 0.008259739 15.731134954 33.522462322
## [296] 1.947069652 9.784609545 0.558580006 5.908440407 21.823630909
## [301] 3.900413946 1.728754714 16.617782022 22.255224379 1.148751662
## [306] 7.185887041 20.162448696 0.275622783 17.205700728 1.387053775
## [311] 15.395128819 15.519644617 13.422796325 3.660205649 3.068556408
## [316] 4.684912487 6.149982186 14.108097180 6.962613165 10.193351470
## [321] 13.222243404 2.707351539 6.172240898 7.283519860 6.389342798
## [326] 44.786796542 20.136311743 36.669018024 8.256779695 3.760542584
## [331] 17.255398636 13.236698117 27.388266119 8.154078796 11.390120629
## [336] 7.301265448 7.772065631 32.763864992 7.443323973 3.312009927
## [341] 3.352804626 33.538878186 3.902104888 11.461934475 0.964886115
## [346] 8.731842655 13.949566445 1.798032476 1.233512177 3.774422402
## [351] 9.382304167 2.111736829 0.525801560 30.079506694 49.034070239
## [356] 5.438189646 11.551337393 1.441474413 4.076259001 3.144421210
## [361] 8.505557607 26.352728325 4.247075447 22.615703148 0.063630536
## [366] 14.266511238 9.980797674 4.527977766 3.022452143 0.520866673
## [371] 0.293621851 2.948842873 8.808621341 16.446566544 24.313404869
## [376] 15.114638767 17.444467618 5.239706463 0.547898812 0.090393530
## [381] 3.863978027 0.743709876 1.029973129 4.906836846 2.063659122
## [386] 7.308538612 17.783760745 3.392070918 0.930455886 6.229273155
## [391] 5.183336041 37.501177395 12.167619811 34.007523580 5.958058746
## [396] 3.761005307 1.671257266 3.366472870 0.226291930 5.255011786
## [401] 0.495127852 55.813587679 3.683448828 12.288938667 9.713600985
## [406] 6.167725106 31.140126733 11.481179595 4.744498689 10.852073915
## [411] 1.093636588 14.842433016 5.698631126 1.414684861 1.927259215
## [416] 1.099944154 0.164197163 2.697523122 25.662546697 16.807680427
## [421] 13.148131612 10.604049572 13.541769934 9.093570569 1.205610749
## [426] 16.332875657 0.304753424 0.424640084 13.329308945 10.047860911
## [431] 2.465227670 15.061178095 3.800391340 24.110219749 5.639378293
## [436] 32.454382776 6.396893356 7.707809703 8.245488386 2.864431189
## [441] 0.048509590 13.693300802 11.864548853 2.542214012 0.955561375
## [446] 16.123333852 19.167918562 7.536029937 1.442973590 12.938238941
## [451] 1.309307613 6.592477574 2.842276390 12.591421874 4.191597095
## [456] 22.691023685 16.677728686 3.312458967 5.473842449 8.747475026
## [461] 21.294913309 9.294648780 18.674169107 0.139954537 36.939618641
## [466] 5.473720790 1.193301585 2.829252784 8.866903777 5.854766835
## [471] 1.711311527 12.721831239 6.224746993 9.673995561 1.628946764
## [476] 8.794675339 16.965263426 14.285994562 2.434519655 0.959885665
## [481] 15.802480708 1.190917385 10.034900359 4.391745655 8.612056203
## [486] 22.932148966 12.583275456 48.367347305 4.913411138 6.534309806
## [491] 3.738910285 7.989067155 3.183958516 15.861052682 17.706386707
## [496] 9.183922158 11.727762874 23.229864108 4.263003776 1.018454581
## [501] 14.732175320 3.895231792 4.437171185 2.578555215 7.787831993
## [506] 37.121044429 12.624721964 17.617890201 9.717156579 13.473674375
## [511] 5.186713934 7.807080010 20.997761337 7.479097461 21.691460779
## [516] 5.141970669 1.385682828 6.018356974 4.555254206 19.021611828
## [521] 0.588115128 1.972770938 4.578461023 22.360268364 6.526631573
## [526] 9.004832892 15.696214740 1.371375080 20.037709027 19.287393763
## [531] 4.372234903 9.472187627 14.934153798 31.665306129 24.539185916
## [536] 6.393650370 4.059590078 1.354967472 4.426185326 5.048884270
## [541] 12.188375676 8.451883057 0.633666543 7.317314660 6.635806356
## [546] 13.146027196 22.415523509 1.505403268 2.513366309 2.568096076
## [551] 10.061018373 14.975702967 4.152755436 2.578360190 21.323746795
## [556] 1.455595623 11.965209273 20.452183596 7.754170429 22.389479371
## [561] 3.819796997 8.409776575 15.815943255 2.785161402 1.501787507
## [566] 4.401009157 12.821312015 25.834638233 2.697928101 58.143282976
## [571] 20.704802795 3.580456190 0.935723729 12.431402113 5.769438581
## [576] 3.858273332 1.885459428 23.909497780 41.359900886 19.476658161
## [581] 0.761086649 12.339415522 3.390123933 4.361836179 7.380292435
## [586] 5.706972368 0.843765796 13.593365615 0.547386491 12.218638211
## [591] 6.043654159 19.696834552 2.396019009 26.935525118 30.647731422
## [596] 8.498426002 50.393968687 8.033875012 9.939597528 1.774125532
## [601] 14.161809828 9.378232527 23.353284242 9.801235459 2.498110738
## [606] 8.867319626 1.414263868 31.206851078 19.120340048 4.541729414
## [611] 6.533801006 0.214421507 1.354523315 64.218840428 15.365191865
## [616] 0.572269663 1.724039783 27.888229860 15.576827153 4.061459480
## [621] 21.284128780 2.436141246 0.609239044 41.304213756 4.504559040
## [626] 10.855949183 1.091263592 4.753044145 2.462583240 9.372608037
## [631] 12.619331190 20.029940046 4.206226081 1.250336175 7.967432318
## [636] 4.711168073 0.985595877 10.776553563 0.299312696 6.315358952
## [641] 0.525451386 20.106147601 2.102489870 5.411940939 4.668971100
## [646] 6.778119965 1.380976848 41.477095539 10.693050084 1.102276137
## [651] 22.540719005 14.783127549 3.692173925 26.733925211 20.165816023
## [656] 11.570677338 6.923915152 14.608831188 5.581377372 7.135699139
## [661] 0.960866520 28.574373869 6.122189523 10.441584093 2.475273067
## [666] 12.306612711 7.016414387 0.251499433 9.745556535 1.628663153
## [671] 2.346888166 8.112379591 4.955730974 6.878294162 0.695180940
## [676] 9.020882267 8.657733057 3.092534896 2.017633312 0.727198618
## [681] 1.949037332 40.592251474 50.915155873 14.373203962 40.540305430
## [686] 25.535127724 8.294592601 14.963082348 6.739558219 8.549939454
## [691] 16.616650558 1.711342083 15.765181779 18.187708388 10.500332005
## [696] 18.575098719 13.153132693 2.271192367 3.713426688 6.470512003
## [701] 11.890756357 0.130534579 9.390270169 22.922872769 1.304654348
## [706] 0.421697272 2.615313224 11.526808703 7.300638088 14.290797539
## [711] 8.623617975 0.597300122 4.447977361 1.115734766 18.498198985
## [716] 4.603671241 1.790513010 9.430766310 5.455887979 10.383399892
## [721] 2.881569837 0.688616285 13.344974588 9.013368279 5.959452624
## [726] 6.010214239 12.408499652 12.195059610 2.910312284 3.578899621
## [731] 15.765470284 2.255318058 31.155269293 7.368804294 0.013433984
## [736] 7.741195820 1.976042981 4.716752525 4.271556237 24.780847768
## [741] 18.887261329 25.977524551 6.217789575 19.056361484 41.277376616
## [746] 0.953964518 10.140476392 21.286399605 4.660799867 12.768735420
## [751] 10.189281902 0.777062987 6.277010483 0.334890767 1.642877944
## [756] 6.614681245 41.668693610 5.313793342 9.517976231 6.240234887
## [761] 1.391559458 3.162966171 17.721225014 1.694201790 9.885492168
## [766] 12.784616968 16.774043488 37.963502312 12.149390587 13.825408909
## [771] 19.177028685 4.106585635 44.588245718 4.624801860 41.902918754
## [776] 2.876800043 18.678703656 2.848867513 6.932071382 11.882153367
## [781] 17.164713851 32.978688179 5.470621120 10.176164982 1.057529412
## [786] 3.526610578 8.024846641 34.639704300 11.160490862 0.613328214
## [791] 12.544748969 9.671451440 3.651501085 8.316068109 12.535260375
## [796] 2.165427500 15.020307375 21.443997456 0.189116147 5.747699267
## [801] 11.277883797 40.723257119 4.921871959 36.436160685 7.511337150
## [806] 6.247859676 2.550048833 2.611449719 12.567065814 9.348018563
## [811] 4.109415001 10.044355560 22.904714289 1.827744842 18.129884693
## [816] 4.827002482 8.686520131 2.783716214 21.112116867 0.887291398
## [821] 10.794319253 13.756672951 12.662859046 2.176942751 10.750821009
## [826] 6.973561422 39.938567484 30.977052522 1.295410722 2.181219570
## [831] 3.494105266 13.852602755 3.087625755 1.236508984 7.231568796
## [836] 21.553678363 6.581433895 5.420925939 3.236703394 5.703658848
## [841] 0.691061922 8.009928623 4.444441022 11.183678982 12.239947142
## [846] 27.955855502 0.428905739 21.311824134 0.257699442 2.841398981
## [851] 5.701567191 12.933980282 2.706857373 8.388339849 2.234968171
## [856] 1.176254773 30.515370442 4.905638937 20.381937268 3.129919302
## [861] 0.448293425 2.668731697 2.351262677 8.327293703 17.599141075
## [866] 10.088133281 9.864915339 29.029412938 0.512237051 1.936138300
## [871] 4.841733184 0.577303887 7.328591765 5.842569917 3.383636537
## [876] 18.883479665 4.260661216 24.405610728 12.790601032 4.323734338
## [881] 24.917445194 7.854578485 20.987510326 22.362939509 2.514911235
## [886] 1.166378800 0.253223018 0.761086664 12.025156077 1.132820956
## [891] 9.486319273 23.969276267 5.598750846 19.321721885 3.111709352
## [896] 8.297999873 7.149304843 2.072617205 6.186925503 0.882443845
## [901] 0.037183516 53.488882647 6.337481244 5.643271757 2.555563524
## [906] 6.474873638 5.748977265 2.456516693 2.779819959 11.667969666
## [911] 36.281762326 17.105081025 9.887988713 10.761686656 4.116882500
## [916] 4.429905511 15.831305775 2.022507801 7.841521240 8.472012855
## [921] 3.073754543 8.047182549 4.259121860 2.267073044 14.432700909
## [926] 21.995575930 2.552655049 6.919034608 14.106591715 6.723822560
## [931] 11.421440215 10.219013141 2.894726614 3.536991558 16.284074484
## [936] 6.917020110 18.144905036 33.725815861 4.037942982 0.369344987
## [941] 7.576571144 1.947553270 5.911521683 3.785720752 10.161048227
## [946] 6.963418780 0.817578447 0.260206336 4.446993396 5.396205932
## [951] 3.470879770 20.508917234 36.846269804 9.519123835 2.352758114
## [956] 9.814928025 7.037517115 4.940517661 8.755766786 3.202088895
## [961] 22.210135142 1.556074489 1.591586680 2.323945150 1.497136699
## [966] 3.834228278 25.155789348 1.547494639 13.428241470 3.435191937
## [971] 8.231649324 6.341166059 15.495474315 13.534544939 14.858896042
## [976] 2.409666397 15.273757911 11.308786645 14.181139385 12.605481576
## [981] 9.873961592 2.042118101 0.825433591 1.759145502 1.160924835
## [986] 12.639798186 6.493785186 23.870821534 7.889760313 16.451546474
## [991] 3.817090533 1.847305712 4.556257254 2.778505692 2.289003297
## [996] 34.499279408 1.303155059 1.746827606 2.571341502 2.437812900
# Rata-rata hasil
mean(sim_5)
## [1] 13.14715
mean(sim_20)
## [1] 13.4504
mean(sim_100)
## [1] 9.645558
mean(sim_1000)
## [1] 10.13295