Soal Latihan PSS
1. Modelkan pendapatan bulanan dari 1000 pegawai yang berdistribusi
normal dengan rata-rata pendapatan Rp10.000.000,- dan standar deviasi
Rp200.000,-.
mu <-10000000
sigma <-200000
n <- 1000
normal_data <-rnorm (n, mean=mu, sd=sigma)
normal_data
## [1] 10385901 9957184 10041531 9751929 9489257 9878404 10083181 10005064
## [9] 10303403 9849978 10170442 10099242 10311178 9799610 9993602 9998530
## [17] 9744543 9418104 9768114 9891367 9972510 9633033 10075037 10185140
## [25] 10313140 9878282 9900680 10243365 10087984 10208433 9601951 10331249
## [33] 9921805 10384673 9689175 9447421 10328743 10084760 10413253 10145763
## [41] 9973226 10144338 10364669 9979414 9677878 9822096 10457350 9877690
## [49] 9864423 10036470 10048742 10032062 9876047 10091744 10135704 10179854
## [57] 10131696 9987703 9875951 10156562 9878428 10129619 10012271 9825774
## [65] 9776120 9813312 10215567 9994766 10072745 9815365 10006404 9971292
## [73] 10359823 10180193 9867765 9920232 10075393 9834646 10213180 10076488
## [81] 9735261 9954624 9683316 9757404 10144773 10011229 9644252 9844292
## [89] 10152321 10005672 9815409 9696545 10213403 9878470 10114227 10158280
## [97] 9910849 10469910 10344691 10240654 10014629 9985003 9757407 10296234
## [105] 10014971 9859082 9919167 9916675 10186583 10085629 10311060 9751163
## [113] 10012451 10206005 9919681 9940607 9708450 9670738 9827062 9928874
## [121] 9966670 10207186 10190140 10288285 10017971 10255897 10350980 9739377
## [129] 10137622 9818189 10043181 10053666 9893956 9811075 10470542 9879057
## [137] 9997004 9621010 10030178 10185432 10295820 9466603 10090140 9610773
## [145] 9945283 9853594 9929133 10243552 10086720 10117106 10088312 10035710
## [153] 9843749 9781596 9855796 9467149 10173548 9894884 9685893 9938265
## [161] 10235990 9875283 10294009 9650477 10000588 9472401 10021881 10292423
## [169] 10238128 10179630 10159510 9825350 9998796 9877101 9636592 9977307
## [177] 9894353 10170200 10135407 9846006 10045672 9686545 10098345 10115198
## [185] 10044014 9994253 9969763 9702843 9942120 9928750 10037000 9670577
## [193] 10349996 10310399 9829830 9835743 10261306 9909290 9976681 9687349
## [201] 9729059 9740566 10267534 9833704 9999169 10285161 10032915 10060225
## [209] 10310667 9749408 9699653 10071883 9968453 10274230 10077233 9871700
## [217] 10370186 10249227 9756026 10175524 10043497 9932826 9718894 9872492
## [225] 10040756 9929482 10105378 10067868 10286174 9919980 9324385 9965423
## [233] 10150849 10204302 10209560 10224226 9897809 10218811 10263395 10300537
## [241] 9833440 10016614 10168415 9746024 10116424 9941680 9842615 10103576
## [249] 10112803 10157733 10227777 9800613 9912690 9908456 9711748 9798010
## [257] 9977583 10258895 9669864 10074813 9708514 9877347 10203974 9840167
## [265] 10020157 9960865 10090832 9831311 10103771 10025188 10155450 10113948
## [273] 10490994 10197971 10174732 9535541 10476002 10212752 10146680 10030647
## [281] 10104395 10242125 9918406 9773517 10148718 9999992 10038370 9983309
## [289] 9804112 9961459 9986287 9908914 10107653 9945084 10047691 10238280
## [297] 9884320 9981518 9665241 10032813 10243199 9865237 9822504 9833959
## [305] 9588066 10039961 9822995 10106067 10309050 9920344 9992990 9989809
## [313] 10139754 9580698 9913143 10028888 10078663 9983357 9701143 9999995
## [321] 9969643 10020958 9983769 10104851 9782361 10384040 10251954 10112370
## [329] 9975052 10055789 9790695 10344572 10086190 10176814 9990031 10253316
## [337] 9650359 10244845 9875787 9951611 9872043 10219379 9947377 10293112
## [345] 9699261 10059496 10152203 10287937 9818710 9901324 9736396 10078872
## [353] 9933309 10269725 10111539 9945855 9817263 10204828 9829308 9747965
## [361] 10098066 9849496 10027991 9671507 10082933 10259316 9556186 10014159
## [369] 10404331 9934378 10143097 10148186 10042858 9998535 9679652 10035073
## [377] 9841262 10153713 9657079 10310970 9597221 9862017 9557526 10069477
## [385] 9687212 9998871 10219693 9752951 9877367 9722758 9721747 10005141
## [393] 10533223 10164510 10090933 9867408 9805498 9857647 10108208 10051780
## [401] 10188526 10392123 10055119 10095101 9853810 9924863 9978860 9780783
## [409] 9869170 9753951 10073190 10215177 10181087 9841654 9959798 9973900
## [417] 9863653 10175027 9762151 9853154 10078173 10311993 10044102 9755678
## [425] 10200137 9898062 9908804 9995280 10279954 10111389 10120924 9956196
## [433] 10184353 9752873 9832194 9877078 10007779 10098623 10384063 9983290
## [441] 10241513 10289734 9872976 10022399 10185554 9904520 9912626 9867017
## [449] 9929011 9877660 10167273 10029142 9560021 10205521 9823000 9912376
## [457] 9985829 9762098 9836824 9902722 10223018 10361199 9955380 9795978
## [465] 10569210 10067095 9939188 10069500 10230865 9984856 9925422 9875470
## [473] 9735653 9900251 10017773 9604052 9876904 9694705 9872454 9927915
## [481] 10045509 10058670 10128330 10120777 9934892 10144376 10326102 9790047
## [489] 10088345 9945592 10209239 10021690 9921354 9800361 10104887 9987717
## [497] 9655391 10008490 10309287 9967656 10153713 9985665 10016604 9900609
## [505] 10283166 10126673 10036970 10045401 9957886 10122972 10019839 9725239
## [513] 9859677 10072879 10351781 9791195 10182889 10160750 9960984 9824586
## [521] 9954528 9956119 9986640 9871131 10105472 10254014 10181858 10236616
## [529] 10021667 9876941 9828202 9957092 9994413 9951320 9692041 10255843
## [537] 10236528 9773468 10163465 9897552 9776990 10236333 10112874 9866126
## [545] 10139983 9874412 9685024 10082805 10107278 9867236 9988484 10293905
## [553] 10005061 10084494 9695363 10208437 9949455 9837245 10246246 10034957
## [561] 10045808 10116738 9829750 9811161 9789049 9909934 10331511 9800896
## [569] 10058233 10014889 10112758 9982947 9751169 10130636 10566768 9901188
## [577] 9764325 9706299 10142268 9932936 9686547 9924451 10053122 10329374
## [585] 9677950 10190904 10368505 10143642 10215834 9976104 10062526 10346337
## [593] 10256384 9937335 9886585 9861692 9671762 10084368 9828854 10205506
## [601] 10081104 9996308 10075294 10092483 10119567 10340738 9943557 10356593
## [609] 9890670 10062882 9832666 9888682 10092578 9932754 10035799 10264250
## [617] 10081929 9792520 9931889 10084893 10274886 10279313 9695924 9760852
## [625] 10116575 10255155 10023388 9986324 9862563 10140495 10219188 10106392
## [633] 10214896 10089069 9870126 9977159 10055541 10372292 9810161 10208701
## [641] 10096693 9934880 9866259 9973030 9927540 10028820 9995057 10127996
## [649] 9994010 10224160 9952309 10148597 10434914 9784464 9942110 10153723
## [657] 10036733 10369767 9762226 9832613 10104110 10357052 10144763 10195209
## [665] 9879558 10414983 10143782 10154761 9997216 9843542 9993647 9810602
## [673] 9765047 9878075 10039753 9931286 9904462 9848671 10050138 10130778
## [681] 9880070 9744100 9885875 10129236 10063283 10005349 10060026 9713732
## [689] 9763771 9669163 9881707 9755904 10319810 9842766 9807651 9921398
## [697] 10057431 9860837 9669478 9575242 10031653 10228541 10152350 10382607
## [705] 9956275 9997546 10027704 9972074 9987039 10010282 9811948 9955783
## [713] 9791050 9912447 9887438 9847521 9810223 9886108 10010444 9765042
## [721] 10226019 9744760 9948664 10253055 10012751 10014075 10066378 10430103
## [729] 9975791 9815846 10161476 9921148 9856059 10287066 10132552 10064971
## [737] 9931623 9912734 10075747 10287387 10478930 10214435 10010276 9567341
## [745] 9970000 9785835 9989638 10134474 10143962 9959578 9784368 9669723
## [753] 9868055 10390348 10004589 10082974 10318038 10066858 10220011 9896092
## [761] 10384009 10020730 9899390 9600008 9911773 10128480 10001624 10082435
## [769] 9885500 10288665 9919206 9594503 9808670 9896352 9965940 9979371
## [777] 10189038 10056173 10065331 9703776 10141105 10086388 10221479 10183315
## [785] 9969938 9861637 9895431 9817143 10193035 9887851 10277600 10069424
## [793] 9886096 10523369 10170224 10036619 10122566 9806349 9927999 10242103
## [801] 9771708 10166851 9986247 9836593 9725579 9688024 9842180 9747012
## [809] 10083657 9678853 10079414 9687010 10296676 9732906 10168824 9966363
## [817] 9836007 10144060 10078950 10208758 10073716 9810587 10149507 10544309
## [825] 10034526 9968222 9958680 10075280 10213076 9649424 10135288 10054636
## [833] 9569443 9881343 9867338 9654714 9771300 9315200 10182310 10082507
## [841] 10287569 10077540 9897861 9914797 9677152 9764839 9673930 10062898
## [849] 9815502 10126766 10071877 10016263 10229405 10189294 10268653 9613009
## [857] 9950581 9844802 10046150 10050878 9989523 9822224 9997049 9780536
## [865] 10012479 9699399 9965567 10016808 9863574 10126931 9563753 9866028
## [873] 10033187 10083797 10166992 10091347 9952570 10031547 10253666 9898147
## [881] 9955559 10131862 10096109 10114680 9895856 10083419 9875842 9887735
## [889] 9922984 10344754 10081085 10048036 10187409 9885025 10445047 9607286
## [897] 10196024 10103749 9983393 10181017 10009811 9740796 10201737 10094308
## [905] 9983152 9919789 9749165 10023815 10291231 9994258 10236083 10063780
## [913] 10162277 10245734 10219956 9783755 10059537 10018192 10001686 10169962
## [921] 10237312 9901428 10071361 9705594 10037658 9874701 10174623 10159782
## [929] 10036470 10035166 9791268 10172562 9936164 9932428 10171043 9817563
## [937] 9912735 9746070 9927600 10185124 9825319 9931882 10156715 9927019
## [945] 9904210 10109232 10018675 10291507 9978048 9862181 10054296 9685975
## [953] 9722454 9746016 9857716 9880259 9850576 9923205 10301355 9940567
## [961] 9669335 9772700 10412247 10219041 9807896 9841300 9878779 10134164
## [969] 9793221 9830641 10036359 9743548 9833563 9657270 9833543 9854638
## [977] 9786184 10052659 10256282 10036543 9792804 10305119 10049971 9955769
## [985] 10011663 10236706 10070477 10272052 9991957 9995762 9854827 9856884
## [993] 9985004 9923104 9679921 10093308 10376518 10003601 9820861 10098787
hist(normal_data, breaks = 30, main = "Histogram Distribusi Normal", xlab = "Jumlah Kejadian", col = "gray")

2.Modelkan jumlah pelanggan yang datang setiap hari ke suatu
restoran yang mengikuti pola distribusi poisson dengan laju kedatangan
pelanggan 35 pelanggan perhari.
lambda <-35 #Pelanggan
n <- 30 #perhari
poisson_data <- rpois(n,lambda)
poisson_data
## [1] 32 39 45 24 35 30 33 44 30 34 36 36 32 47 38 37 31 36 40 38 26 44 37 26 46
## [26] 31 31 36 33 35
hist(poisson_data, breaks = 30, main = "Histogram Distribusi Poisson", xlab = "Jumlah Kejadian", col = "gray")

3. Buatlah dua kasus Anda sendiri dengan melibatkan distribusi
variabel random dari teori yang telah dipelajari.
3b Distribusi Binomial “Modelkan jumlah pegawai yang mendapatkan
bonus tahunan dalam 12 tahun kedepan dalam suatu perusahaan, di mana
setiap pegawai memiliki peluang 60% untuk mendapatkan bonus. Asumsikan
terdapat 50 pegawai dalam perusahaan tersebut.”
n <- 12
n_pegawai <- 50 # Jumlah pegawai
p_bonus <- 0.6 # Probabilitas mendapatkan bonus
binomial_data <- rbinom(n, size = n_pegawai, prob = p_bonus)
binomial_data
## [1] 32 29 33 26 26 30 27 32 35 31 30 31
hist (binomial_data, breaks = 30, main = "Histogram Distribusi Binomial", xlab= "Jumlah Bonus", col="gray")
