# UNIVERSIDAD NACIONAL DEL ALTIPLANO
# INGENIERIA ESTADISTICA E INFORMATICA
# CURSO: ESTADISTICA BAYESIANA
### Probabilidad Normal
### ===================
#Generacion de Valores Aleatorios
rnorm(10, mean=5, sd=2)
## [1] 0.549426 5.812510 3.826758 2.441972 4.972287 2.067401 6.866309 3.189944
## [9] 2.868518 4.854870
#Densidad Normal
dnorm(1, mean=5, sd=2)
## [1] 0.02699548
#hist(rnorm(1000, mean=5, sd=2), freq = F)
x <- rnorm (1000, mean = 5, sd=2)
hist(x, freq = F)
points(x, dnorm(x,5,2))
#Funcion de Distribucion , F(x)
pnorm(q=12, 5, 2)
## [1] 0.9997674
plot(x, pnorm(x,5,2))
#Cuantiles de la Normal
qnorm(p=0.3085375,5,2)
## [1] 4
### Probabilidad Binomial
### =====================
#Generacion de Valores Aleatorios
rbinom(100,size=6, prob = 0.5)
## [1] 4 3 3 4 3 3 0 3 4 3 3 3 3 2 1 1 2 3 2 2 4 4 2 4 2 3 3 2 2 2 3 5 4 2 2 3 5
## [38] 3 1 3 5 2 2 3 2 2 3 2 3 4 2 4 2 4 2 2 1 3 3 1 4 5 1 3 4 3 3 5 4 0 4 4 2 3
## [75] 3 3 4 2 4 3 2 3 4 4 4 4 3 5 5 3 5 3 3 2 2 3 3 5 3 2
#Densidad Binomial
dbinom(3, size = 5, prob = 0.5)
## [1] 0.3125
qbinom(p=0.4, 5, 0.5)
## [1] 2
pbinom(q=2, 5, 0.5)
## [1] 0.5
B<- rbinom(1000, size = 5, prob = 0.5)
#Funcion de la Binomial
plot(B,dbinom(B,5,0.5))
hist(B,)
### Probabilidad de Poisson
### =======================
#Generacion de Valores Aleatorios
rpois(10,lambda = 3)
## [1] 3 2 4 1 5 2 2 6 2 1
hist(rpois(1000,lambda = 10))
### Probabilidad Ghi2
### =================
rchisq(1000,df=10)
## [1] 12.0071183 5.9087811 5.0588280 4.7689849 14.8333713 5.2098098
## [7] 5.6430463 7.8646369 8.7577047 5.8237488 14.2942304 9.0027535
## [13] 6.1230024 4.6421311 11.1612504 7.7841632 13.2552503 13.1098480
## [19] 6.7827735 9.2852323 4.0885135 15.8427382 13.9622420 15.0346654
## [25] 16.1850492 8.5856844 7.2024507 8.8752748 4.4356577 12.5076546
## [31] 12.0917325 15.0254188 8.5803484 5.0805816 10.0995190 4.8326464
## [37] 2.9414673 2.1854153 19.2608630 22.1163983 6.4895177 11.6970078
## [43] 5.5402427 13.8555520 5.4908919 5.6722913 15.3592614 7.3974095
## [49] 5.6210878 9.4287126 13.6226635 8.9385236 16.9878067 4.9955828
## [55] 9.6932058 20.0246306 5.0252536 17.1072326 6.4234256 17.6635736
## [61] 1.8401075 4.3386419 13.5060973 11.9801093 6.7047476 5.7299996
## [67] 5.4803400 4.1804007 17.6861675 16.5672738 16.7343831 9.5157642
## [73] 16.7246042 12.1373342 9.3603380 9.7476532 15.7600655 9.6360482
## [79] 11.2468286 8.6919934 10.5059034 10.3385923 16.8955906 4.2655818
## [85] 5.1168222 7.5745790 10.5017613 7.6636476 20.0736653 10.2728182
## [91] 9.9493092 10.9425487 14.0023871 4.8985433 9.5010237 9.4033718
## [97] 18.0519813 11.8346578 12.4920407 4.5168228 5.9766560 10.5168802
## [103] 11.0666127 7.0776802 4.2238934 6.2467584 12.3111397 12.2947563
## [109] 4.6435075 12.7639952 8.1063378 16.6268824 12.1327593 10.5091357
## [115] 5.9540155 13.1600414 6.5793523 5.3845343 5.5489991 8.1246700
## [121] 5.9001767 13.7053182 12.6856835 6.9827329 12.9070071 8.6303763
## [127] 2.9665759 6.5968512 8.3194944 10.3103693 11.8487018 7.4825834
## [133] 11.1168481 12.9866833 6.0485230 17.0362536 11.7519228 11.0300881
## [139] 8.5669532 5.8564936 8.4885501 14.2320233 4.6853713 7.9992020
## [145] 6.7470361 5.8435146 8.5585986 11.3453443 9.3897049 11.8949473
## [151] 5.9656278 6.0852750 4.5331009 6.7202492 13.2538040 12.9169014
## [157] 4.5196504 5.6168144 9.6628756 3.7688372 10.1274946 17.5092748
## [163] 5.8360401 20.1351553 9.1143021 4.3422637 16.2340762 8.9884063
## [169] 17.9227291 16.9149988 13.6184114 7.1966009 9.2519249 16.3285617
## [175] 4.8545859 15.6527500 9.0609804 10.2448129 10.2148125 13.0610923
## [181] 14.3314593 7.6444767 5.4372398 5.6209946 12.2276484 12.1590191
## [187] 12.2130661 3.9877470 13.8976029 10.8331584 24.5637252 9.7523939
## [193] 7.1047235 6.2982980 5.4981086 12.6789399 3.3773880 10.8449305
## [199] 8.4820240 14.1421633 17.9250014 12.3914470 5.0538864 8.8312650
## [205] 6.0656568 4.6691439 10.7347759 3.8442899 13.2485492 12.7924954
## [211] 16.0263085 10.8370954 13.5665905 5.4723222 8.6175822 10.9270651
## [217] 12.4099687 4.9623269 9.9300615 6.8675336 16.4316166 11.2807981
## [223] 4.5178955 7.2021272 5.8416730 11.5556447 11.7054946 5.5097330
## [229] 6.4210968 6.1000243 5.3365602 12.9681515 13.0251445 10.4494798
## [235] 7.2398825 10.7521213 5.5264527 4.7669077 5.6291107 12.0117259
## [241] 9.3282920 11.3802170 9.7355368 10.9191130 9.1635965 7.1324520
## [247] 4.5911432 8.8752999 8.0013515 10.6769861 15.4210495 7.5363065
## [253] 2.6314701 9.2194440 7.4949081 13.3171284 16.3419786 8.7760296
## [259] 14.8657406 13.7221977 5.6361538 7.0845830 15.5458479 16.6241747
## [265] 14.5023998 11.4107724 5.6679013 8.8505979 7.1494263 15.4970898
## [271] 11.4928110 8.6226141 14.0916357 7.3436896 3.7136788 12.0261257
## [277] 4.6798918 9.4835699 9.6481813 7.6935771 9.7795923 14.3125741
## [283] 11.4182620 17.0309283 12.2919832 9.3369614 3.9385247 11.7892211
## [289] 14.9234685 10.7660792 12.0812702 11.6811178 15.2450406 3.8619700
## [295] 12.0625384 9.9395309 8.9908070 11.2754862 3.3081427 6.9385785
## [301] 11.1412560 11.5372002 14.7250233 9.1946174 13.9226333 8.0387156
## [307] 2.2226967 12.2529745 10.6776335 12.5438815 12.2810557 16.2296075
## [313] 9.7411188 11.8533240 8.1221675 12.2297186 15.8712323 19.5436572
## [319] 11.1716250 4.4828337 10.4531759 15.2939830 10.2845123 10.2485109
## [325] 6.3112190 11.2389008 11.4011186 18.8225695 10.7951204 12.1688144
## [331] 14.3920567 8.8036049 11.1388113 3.0516869 6.3800092 16.2033397
## [337] 10.1694719 8.8220303 6.3878024 9.6952451 12.5453617 19.1470233
## [343] 5.5773811 20.9177400 8.7723348 8.6146234 9.4562001 11.7577050
## [349] 6.4009221 7.5612872 14.4595015 5.2237228 7.0912207 13.7989873
## [355] 12.8215995 16.4749533 16.1156703 7.9552529 5.1178030 9.7892339
## [361] 14.4445338 18.4548147 7.6714525 8.8484225 7.4050160 10.5629287
## [367] 8.6724437 8.1067235 10.2380020 8.0152578 7.5287423 16.2907956
## [373] 8.4787215 8.9979766 13.5752169 11.9536859 12.8043134 7.9362980
## [379] 7.3433203 11.0000693 11.2655604 7.5364752 11.6832874 12.9589403
## [385] 4.5011554 7.8089554 12.0936015 8.0686664 7.5886681 5.6949073
## [391] 16.4121346 9.7482492 2.9487503 7.5445544 5.8210179 11.6849699
## [397] 6.0111914 3.0481251 7.7690760 3.4306514 7.4103484 14.2167984
## [403] 11.0995090 8.1245866 3.1438223 13.1990097 13.9709213 11.6690729
## [409] 7.4780922 9.7480213 17.7365240 11.6473513 11.7362106 11.3639208
## [415] 9.8643273 7.2694021 15.2530887 15.1543696 10.0252648 8.9715625
## [421] 7.1334445 10.2750596 7.9143501 7.3638776 9.8493234 8.6794102
## [427] 2.5759857 6.6687176 11.0961287 12.5706488 15.3555521 7.0864454
## [433] 9.3093479 11.2101765 13.0908909 8.5381834 9.7750763 25.3753627
## [439] 6.7966780 11.4892743 7.6779073 9.4366727 14.4364042 17.0634500
## [445] 13.9057675 10.4621057 9.7688245 6.6969753 8.4645842 16.4570997
## [451] 7.0043548 13.4111273 2.3846609 11.4094850 3.5864007 18.8021556
## [457] 13.0327391 8.4159415 6.0131674 6.6249315 4.8830979 3.3386408
## [463] 15.4401601 21.3581073 7.6426918 7.4251647 12.8150344 13.2319186
## [469] 12.3524856 7.8286556 13.3507652 13.5831238 11.1902484 14.4970622
## [475] 18.6122486 11.3068135 3.1195266 6.0656626 14.9251400 9.7336097
## [481] 5.9413738 18.7718079 7.0796044 5.9484159 11.6589195 3.4754749
## [487] 16.2316261 4.4265041 12.0020572 12.0452980 5.8417984 3.8911799
## [493] 7.5221225 13.6053995 10.7468382 16.0076201 7.0859508 12.5594787
## [499] 5.1027309 16.1456847 10.6281349 16.1166729 8.1296678 10.5851169
## [505] 10.1357533 13.1840639 15.1193755 7.8224347 12.9847702 6.2908313
## [511] 6.0690339 3.9671737 3.9792603 6.8018660 8.1038653 9.6725042
## [517] 23.1858852 8.1461182 10.7552903 22.0056145 6.6914799 6.4146131
## [523] 10.0843858 11.4606919 17.7855996 19.8632993 17.1410835 5.7719296
## [529] 5.9873042 7.8034211 8.8866905 11.7075160 9.0472285 9.8329676
## [535] 7.2464120 7.7653118 6.7881611 7.7454014 13.9323390 4.1400768
## [541] 18.1244238 11.9571021 9.1815587 8.5196890 12.6655400 5.1814930
## [547] 3.6838805 9.5927056 13.6791926 14.4819113 5.7206208 6.1958595
## [553] 14.6942804 12.9371577 8.7111336 7.0172557 5.8971947 9.7894242
## [559] 3.2732538 14.1971748 11.9480433 10.2531461 8.5940752 12.7631128
## [565] 12.5455261 9.7883277 12.3041382 11.3847871 10.7319037 13.3843250
## [571] 13.4034871 13.4942014 6.5815077 7.5128121 12.9420088 8.5888169
## [577] 5.2048083 11.2133926 14.3849425 11.2776038 15.6236504 19.0514858
## [583] 15.6877183 6.6583646 4.7035171 11.1439479 1.0995932 13.3660036
## [589] 6.1818918 18.2831994 9.1817872 11.2386397 10.5514993 16.9885884
## [595] 8.0486401 8.3684077 9.5753630 8.9358647 5.0835768 13.7143944
## [601] 4.7017551 6.7914961 9.6594566 13.5508537 6.4071428 9.1230271
## [607] 10.6551943 11.1611457 14.3563064 10.5832973 3.2087236 11.5227935
## [613] 11.4696696 9.3687864 6.0377919 12.8763859 11.0156711 8.9297290
## [619] 11.0088334 4.3645250 4.3844658 7.3125673 20.1008886 9.9765186
## [625] 10.7031994 8.5706430 7.8370683 12.6596179 11.7674229 13.5653889
## [631] 14.8388875 8.8852578 9.1303443 13.8623798 8.6259272 14.9710484
## [637] 4.6838533 20.7941661 8.2600846 6.3623886 12.6267068 7.1253529
## [643] 3.3555568 14.8954476 8.7745938 15.2989026 0.9862745 6.9096264
## [649] 16.3126497 7.1865601 19.7713901 14.0969856 11.3123166 7.8558909
## [655] 25.3118262 12.6655325 7.8532492 5.7428333 7.8329585 10.1333008
## [661] 18.7315195 8.4183224 13.9757468 8.8339706 2.8602892 11.7048530
## [667] 18.7320048 11.3401633 15.6022195 6.6090091 7.4778300 6.4815384
## [673] 6.6715646 5.9265098 6.4534501 12.2522940 11.3842037 6.5166804
## [679] 11.7126453 2.4561829 7.0436771 9.4644082 7.3501927 11.6504941
## [685] 6.1894319 10.1738164 13.3349774 7.9796027 4.7181476 10.0036574
## [691] 12.7301480 11.7656734 7.5310721 13.3796042 7.9656031 8.9131030
## [697] 6.6269155 12.7333428 13.8908275 5.0914207 10.3564485 4.1012487
## [703] 15.4626697 14.5072653 6.0472271 5.4874102 7.0584302 7.5950951
## [709] 7.3311492 6.7907016 1.9342817 14.9275231 18.6508819 9.6641289
## [715] 10.4641732 5.0804486 2.2034469 14.6485275 11.5748862 7.5186761
## [721] 14.3877003 10.6832191 9.0596558 6.5558398 3.4466595 12.1225055
## [727] 19.1665321 12.1516775 19.2123311 8.9059597 13.8964689 10.1880593
## [733] 6.8781699 5.6701215 6.7472048 10.0913040 14.0447252 2.2700234
## [739] 6.3389086 8.8089444 13.3940744 7.5192974 5.2321796 6.7343459
## [745] 9.3339055 10.8701693 8.3407795 10.6548282 8.6858104 11.1847175
## [751] 11.6244826 11.3789365 6.4760139 15.3142768 11.1552515 5.5814480
## [757] 8.9012047 3.4019438 7.3682996 7.9606910 16.3176269 5.2133258
## [763] 18.1661067 6.1170841 13.8445180 8.9979820 11.3015795 14.2239948
## [769] 7.8010057 10.5020055 8.3057883 14.9563085 12.3815112 8.1969794
## [775] 12.2185306 8.1021991 11.6167649 2.7351912 9.2209905 16.5766997
## [781] 5.9148776 10.4655645 5.9604509 22.8714164 9.5331092 18.8193146
## [787] 12.3888641 7.2322244 6.6220470 15.2269715 8.3434034 10.8563060
## [793] 24.0692773 13.7239326 5.8082583 5.8126113 7.0890116 1.9070387
## [799] 7.2930786 10.0650964 11.1134821 7.2866178 4.5039581 7.0641694
## [805] 4.6022710 6.8584933 13.6648837 12.2780300 8.8674747 8.6551511
## [811] 16.2045654 3.2796475 13.8609494 11.1194556 9.5889709 15.5643204
## [817] 8.8021472 5.1383859 7.3549517 11.9123965 9.0472212 11.6766092
## [823] 2.7918045 9.0536767 11.7415266 8.7446216 2.7223019 7.4774018
## [829] 3.4106800 7.5398957 10.1541098 7.2167513 21.6275719 8.6935653
## [835] 8.3132290 2.6997832 8.3042751 14.6423771 4.6463968 10.9416167
## [841] 5.7649409 3.6257508 20.8083079 3.6838394 11.4619798 11.1756266
## [847] 3.9010050 17.0247699 5.8231523 12.4622162 4.7823935 8.7400771
## [853] 2.6442037 7.9133838 9.5049323 12.7912232 12.7386019 10.8989506
## [859] 10.7199819 8.2827530 14.2545189 12.8095664 5.9122518 9.1406895
## [865] 10.8611703 4.9114035 11.4385166 9.7415743 5.6692231 19.0326746
## [871] 6.6316447 7.2938786 7.5617695 6.3916525 12.5404039 8.9755776
## [877] 3.9840170 16.9442161 6.9117624 15.1469714 16.9531931 9.9391640
## [883] 16.8742176 10.8826309 7.8903394 6.3026460 3.8536297 13.8176104
## [889] 7.3331820 7.0560326 7.5915383 13.9233567 9.2471772 5.4473195
## [895] 5.4036105 13.2273904 10.2316814 10.1616028 13.1029227 13.6228250
## [901] 14.9543355 16.0144567 9.1391798 4.6032669 8.6783753 3.1964946
## [907] 14.3217750 7.8237437 5.1880842 11.4481015 10.1998030 2.6658340
## [913] 4.2614697 7.6861736 11.2149455 12.2370596 11.3969483 9.6226058
## [919] 4.1354166 3.4480463 28.3672621 8.4095986 9.0120145 11.1342474
## [925] 4.7731018 10.3684647 2.6802957 10.5662547 7.7713027 6.6944041
## [931] 5.0346168 11.5064489 7.7333751 7.2133688 17.4909541 22.6390933
## [937] 15.7318840 12.9783046 13.8275805 14.9677896 11.6263538 13.8613388
## [943] 9.2319066 3.7635008 8.4777476 7.9682382 8.4877935 18.9486880
## [949] 3.3580330 9.5635756 14.9409514 16.2646981 7.3803412 6.3859290
## [955] 15.0405945 12.9725353 4.7511351 10.2334323 7.3858171 7.9752009
## [961] 15.0064188 8.1897741 10.7411950 9.2573930 4.0626765 8.4115843
## [967] 9.4436239 3.4747451 3.9424717 4.9831387 8.6779065 18.4894011
## [973] 13.8702580 7.8643469 6.3461426 7.7282854 15.8351137 2.2361202
## [979] 10.8835851 11.4118622 2.9615422 6.3156706 6.2335578 8.7198012
## [985] 8.3013404 3.9199564 11.2442097 7.5537656 4.3164756 8.0399325
## [991] 7.0467594 7.4089723 11.7649089 2.6926382 8.0896142 4.5233265
## [997] 5.5846031 9.4711730 4.3764242 9.3446966
#Funcion de la Ghi2
hist(rchisq(1000,df=10))
### Probabilidad de T-Student
### =========================
rt(10,30)
## [1] -0.16969476 0.29834822 0.38838078 1.12939714 1.99822168 0.07539336
## [7] 1.02928190 -0.05752811 1.49578479 -1.72579389
qt(0.95,df=20)
## [1] 1.724718
#Funcion de la T-Student
hist(rt(1000,30))
### Probabilidad Unifrome
### =====================
#Funcion Uniforme
hist(runif(1000,-1,1))
