beta distribution

dbeta(0.35,6,4)
## [1] 0.7269605
pbeta(0.8,6,4)
## [1] 0.9143583
1-pbeta(0.6,6,4)
## [1] 0.5173903
w=pbeta(0.8,6,4)-pbeta(0.6,6,4);w
## [1] 0.4317486
qbeta(0.85,6,4)
## [1] 0.7586159
set.seed(12345)
rbeta(100,6,4)
##   [1] 0.4925148 0.4685677 0.6190551 0.6771314 0.8736540 0.4839499 0.6475726
##   [8] 0.6489185 0.7510915 0.6202555 0.5330513 0.5049688 0.7249359 0.4474909
##  [15] 0.7460447 0.6568883 0.5463302 0.4548364 0.7080948 0.8410914 0.8468154
##  [22] 0.6817545 0.4858221 0.4874106 0.6281877 0.4484834 0.2018033 0.2822763
##  [29] 0.5544686 0.5104665 0.6556329 0.8549103 0.5954575 0.3849538 0.9296372
##  [36] 0.7723116 0.4235814 0.4400584 0.8225235 0.4959827 0.4929633 0.8078794
##  [43] 0.6913396 0.5905457 0.5365675 0.7123473 0.5501395 0.4721280 0.4461286
##  [50] 0.9268564 0.5734213 0.8128521 0.4986743 0.2908393 0.6988670 0.8753225
##  [57] 0.4333634 0.5056067 0.8063209 0.5903641 0.7302845 0.7706901 0.3289433
##  [64] 0.4224883 0.4456417 0.7344785 0.5132870 0.4066781 0.4810005 0.4022595
##  [71] 0.6523219 0.4167492 0.2359852 0.4758413 0.6529244 0.5018702 0.4459162
##  [78] 0.7578671 0.7412284 0.6669353 0.7603952 0.4728740 0.6855823 0.1824200
##  [85] 0.7009491 0.7160938 0.5599933 0.7864043 0.5233984 0.8103845 0.5749487
##  [92] 0.6906345 0.6535382 0.2976903 0.6762318 0.5422088 0.7970529 0.8102876
##  [99] 0.3578815 0.3460196

Exponential distribution

dexp(3,0.5)
## [1] 0.1115651
1-pexp(5,0.5)
## [1] 0.082085
set.seed(12345)
rexp(1000,0.5)
##    [1]  0.883615585  1.054945511  1.616934629  0.036897343  0.910821015
##    [6]  0.047876279 12.804378475  2.515921043  1.924376174  3.636006079
##   [11]  0.452975022  0.893525823  2.504922241  0.794174558  0.176231458
##   [16]  3.444328406 10.769726846  3.775987856  0.727334493  2.347127350
##   [21]  2.279298922  0.855932194  2.917094875  1.128773122  2.458237083
##   [26]  1.463744335  1.956091748  5.605420881  0.502171188  0.436721868
##   [31]  3.464683734  0.919087887  4.729636501  1.714264510  1.455768896
##   [36]  0.303526155  0.207192708  0.700818550  2.369784320  2.072734669
##   [41]  6.633264005  0.475790156  0.707414910  3.174160093  0.011988554
##   [46]  7.388401787  3.084779147  1.826548399  1.302627451  0.009378569
##   [51]  1.214290503  5.654435933  0.403713127  0.859119522  0.055382613
##   [56]  0.880466020  0.999785080  5.219379846  2.568901282  1.742017586
##   [61]  0.469014662  0.722771173  0.549817731  0.298149054  0.437904179
##   [66]  2.453851445  1.021084178  2.424184304  1.179888254  0.815068960
##   [71]  8.740563370  1.952630915  0.237826933  0.059670241  5.029662672
##   [76]  0.733002295  0.839888198  1.200926216  0.258746488  1.097053155
##   [81]  5.685824781  0.687672563  1.251068488  0.652644956  0.966761759
##   [86]  3.733242985  5.280301016  1.231039964  0.087110542  0.774162707
##   [91]  2.976384914  0.688211013  0.515881916  0.236171791  1.182684818
##   [96]  2.202468323  4.109031487  1.139122497  0.732205003  2.220765711
##  [101]  0.962642062  0.379608004  0.527378747  1.627633584  2.552817350
##  [106]  0.260909564  2.418765573  1.003063372  0.816806702  1.102488454
##  [111]  3.453351322  2.665972596  3.912632573  1.461499356  0.481870152
##  [116]  3.386779025  3.281535286  1.016253029  0.425265392  0.009605953
##  [121]  3.407890638  4.870480478  5.122920658  4.323508147  0.224393330
##  [126]  0.605273629  1.753995869  0.782019532  2.407654013  1.473989891
##  [131]  0.453407789  0.139632553  0.503766467  3.499340512  4.287450480
##  [136]  0.138302119  0.984305066  2.034829054  1.840277415  0.288003396
##  [141]  2.352010553  0.066254565  0.527660583  1.257125906  1.137510794
##  [146]  0.505324266  0.702574854  0.466890114  1.162683092  4.203926549
##  [151]  0.023364471  3.710842650  4.822106574  1.302950762  1.246234840
##  [156]  0.115115903  5.259115125  0.764142607  3.130015630  1.929076904
##  [161]  3.268250987  0.040770989  2.076710381  0.176181566  5.291103642
##  [166]  7.383115332  1.594473720  2.675509609  4.293341566  1.186126257
##  [171]  0.025300972  0.074495276  0.821839806  1.326476332  5.938195411
##  [176]  1.259508576  2.794114687  6.917229682  0.394629127  0.833162586
##  [181]  0.613762639  0.309655874  0.713142132  4.132234912  3.244138589
##  [186]  2.593715850  1.694438585  2.308780705  0.730599947  1.447591457
##  [191]  0.433775604  0.476450797  2.614487529  2.621495500  0.022001598
##  [196]  3.342938326  3.312536182  0.946555354  0.699389051  4.241241119
##  [201]  0.918795990  2.189275724  0.713093351  0.506329116  1.180781112
##  [206]  0.061433287  0.738896147  0.489509008  0.881201803  0.340741609
##  [211]  0.301090519  5.766441762  1.148090221  3.667836007  3.465822376
##  [216]  1.722532282  0.869259552  0.352128583  0.285935904  0.121826120
##  [221]  1.138184560  0.861838896  1.985380913  1.848365683  2.365870487
##  [226]  1.840007147  0.712222193  1.137197147  0.261355480  0.044495583
##  [231]  0.232891837  2.015714260  3.962425794  2.006445065  2.431169212
##  [236]  0.021231149  2.788672406  4.574257347  1.706176341  0.384797546
##  [241]  3.315397985  0.329180858  4.670422021  0.167584530  0.867778478
##  [246]  6.155054956  8.208329122  0.962465725  1.080596265  0.154712759
##  [251]  2.491385892  1.556096684  1.525258636  3.894206233  1.396695621
##  [256]  2.499357622  1.374398421  0.374877255  0.495407205  5.976090913
##  [261]  6.266229093  0.269210174  7.030132006  0.151738729  1.229016130
##  [266]  1.236308975  9.136166490  0.733629202  1.932561997  9.882255289
##  [271]  1.038741301  2.586625477  2.723146999  1.290466080  0.019439966
##  [276]  0.785027832  0.354851781  5.099754665  0.125039939  0.302091517
##  [281]  0.264566939  2.566142822  0.418481138  2.397317855  1.253906341
##  [286]  1.724606212  1.945752075  2.722255049  1.103546433  0.562048360
##  [291]  1.470471905  1.887757514  0.939562096  1.102641629  0.392242040
##  [296]  4.494283111  1.668059856  0.135288223  2.561449304  0.576563368
##  [301]  3.071634974  0.634430581  1.118709097  1.262186992  0.458846134
##  [306]  1.029516481  1.096933347  0.290222534  1.366462246  0.936890844
##  [311]  4.582896527  0.541989842  2.549392991  0.990908232  0.957953845
##  [316]  2.360019920  2.098800374  0.691213394  1.969577651  0.736446862
##  [321]  2.943549371  1.141548742  1.045695191  3.911788005  0.614246854
##  [326]  1.777656723  1.812425611  0.294892827  0.603621759  2.234440561
##  [331]  0.066538929  0.609137408  0.741865166  1.292739173  4.510283180
##  [336]  2.635283006  1.488921510  1.946434900  3.517649433  0.151569942
##  [341]  7.145481061  0.491810805  0.411675664  1.056916370  0.614761949
##  [346]  0.357390470  3.484374080  4.924181621  0.728163979  2.255861834
##  [351]  4.239848155  4.331679936  0.260980104  0.728323616  3.843210805
##  [356]  1.511359569  0.720356984  3.640831594  0.163110625  3.118820080
##  [361]  1.337983513  3.495697862  2.060067110  1.113855183  3.239392229
##  [366]  0.792475441  0.621487801  0.888086370  3.397797018  6.786950871
##  [371]  0.291560293  4.180738472  1.519520441  0.720830141  3.713587257
##  [376]  1.126513546  0.797052250  8.981950499  0.015628323  0.924236840
##  [381]  2.024518540  1.281996581  0.628330169  1.613428399  0.278149901
##  [386]  6.377105951  2.354696494  0.415332234  0.248554536  0.314615944
##  [391]  1.328423558  0.190773278  0.483154915  1.647199584  4.287522640
##  [396]  4.712776024  1.542935802  3.078009530  0.037122204  0.909823766
##  [401]  1.913870044  1.384233947  0.024623883  0.730344845  0.019976170
##  [406]  1.298558498  2.010701571  0.731046680  0.470960985  0.607343332
##  [411]  0.323717035  1.352279254  3.093082685  0.120461583  0.582957946
##  [416]  1.469394404  0.628473271  0.330193439  0.572829003  8.158039134
##  [421]  4.218281325  0.273216785  2.024926932  0.710220347  4.486346546
##  [426]  0.174765416  1.318182161  0.683487344  0.811639710  0.640384672
##  [431]  1.550430901  6.525610185 10.219789240  1.032844490  1.127922791
##  [436]  1.879915026  1.777836900  4.439689066  0.889789658  3.002418984
##  [441]  1.119285749  0.477499581  0.469388124  0.045086689  2.331623213
##  [446]  3.636705886  1.501046237  2.214487031  6.979893316  7.453472655
##  [451]  1.497537017  0.140272751  0.969171301  0.558636709  0.487265858
##  [456]  0.862776572  0.997614893  4.700496086  1.478317903  0.076294072
##  [461]  0.878462581  2.010113962  0.989204251  0.302238034  0.034287924
##  [466]  1.537769051  1.116415990  0.854506473  0.023604254  2.126232648
##  [471]  0.410586065  0.775131730  3.827401616  2.518989550  1.886778958
##  [476]  0.024417229  2.088554684  1.301838242  1.150550775  2.391313272
##  [481]  0.763274609  0.431412748  0.190336931  0.423458835  0.413867616
##  [486]  1.998752000  0.414442743  2.793485781  1.503580961  0.939946392
##  [491]  0.049713388  0.447758160  4.376606673  1.534647766  1.656897051
##  [496]  1.184878987  2.032588651  2.041357323  1.026394315  4.371958473
##  [501]  0.151620732  3.424061950  0.442923161  2.422947927  2.982634839
##  [506]  0.106432498  0.819116165  3.792823586  6.917418271  2.049470078
##  [511]  3.588954381  1.565043482  0.766645171  1.612125086  0.461213095
##  [516]  0.062109335  1.680974167  0.017745242  0.328203216  3.440123755
##  [521]  0.462458438  0.426437654  3.191010158  0.479102891  0.915028892
##  [526]  0.440473720  4.058745432  5.165949482  2.173378958  0.645768363
##  [531]  4.257690810  0.272446884  0.600361319  1.151341007  6.994063776
##  [536]  0.225622090  0.945907666  2.670439130  0.163424971  0.917821615
##  [541]  1.375211568  2.369039416  0.033343679  3.380869709  3.677414074
##  [546]  5.262263257  8.568619176  1.847538276  3.198867000  1.488524567
##  [551]  1.048405156  4.614816990  1.659288937  6.905006274  2.043422921
##  [556]  0.240527821  1.370511991  3.473543878  0.240282921  0.965531539
##  [561]  1.628381194  2.094666338  0.551131309  2.097841199  5.332918685
##  [566]  0.842605533  2.527174441  0.199423082  0.249376080  1.620142562
##  [571]  3.795612920  5.142477911  1.658293903  0.582453673  3.288957320
##  [576]  0.250047203  7.343494009  2.206182316  2.206781415  0.476670865
##  [581]  1.403838653  0.828534307  0.260355254  1.187874278  0.236238201
##  [586]  1.861417225  2.096260838  1.577581339  3.194377501  1.626014986
##  [591]  0.067279678  2.006712908  0.041598842  0.699971317  2.676435208
##  [596]  4.712873790  1.066889165  0.334117438  1.073096521  0.220119088
##  [601]  0.583968737  0.253733723  2.633151334  0.361384310  0.169763717
##  [606]  1.214519545  0.493310807  7.734700899  0.967634001  2.665841848
##  [611]  7.934045326  0.354749692  1.526831226  3.047876535  0.310519649
##  [616]  2.407667475  2.914151747  4.647097599  1.374854594 10.190905210
##  [621]  1.418986313  3.558657788  0.828452658  0.476658974  1.238169111
##  [626]  0.166765135  6.956261020  0.950694994  2.647006394  1.030285838
##  [631]  7.853920381  3.248155281  4.547911024  0.667442416  0.627049129
##  [636]  0.069410650  1.114377510  0.770434198  1.228227224  2.917893756
##  [641]  1.446996164  0.906887718  0.640817367  3.762001048  1.064403318
##  [646]  1.174043196  2.098562667  1.900490474  0.066389235  0.019463935
##  [651]  0.354939874  0.465816083  4.994246188  2.239177415  0.019375236
##  [656]  6.016372054  1.978502675  1.192420448  2.362763442  1.614570554
##  [661]  6.043997803  0.043584447  2.405483885  2.298352500  0.840567137
##  [666]  1.480621836  0.252333673  0.157338933  4.280971766  0.017089549
##  [671]  1.338566658  2.787965681  6.674857825  2.549185239  0.861979038
##  [676] 13.975501976  1.936221508  1.223825214  1.984181518  1.077058756
##  [681]  1.909707675  0.096211564  1.040924757  5.273109074  3.433210548
##  [686]  3.620175358  0.103992100  0.580203622  1.499431567  2.645494539
##  [691]  0.792276936  3.874804836  4.148643181  0.343438653  1.788830104
##  [696]  3.211618919  2.493412124  4.690139185  2.352207724  0.099771301
##  [701]  0.814426806  1.543870739  2.131233693  0.397618515  0.731195240
##  [706]  1.470738873  0.088470022  2.428465296  4.990104515  5.791282403
##  [711]  1.553542098  1.070886974  0.803773439  5.916406656  1.519065898
##  [716] 10.417572114  0.414679194  5.186571080  1.056506435  2.041053556
##  [721]  0.960627858  0.569046115  2.758696698  1.154119018  0.270924008
##  [726]  1.393466080  6.799833104  1.212933604  0.335103398  0.341932892
##  [731]  1.954502167  0.307165041  1.515405155  1.553790849  0.122264097
##  [736]  0.447580876  2.187271047  0.705139866  3.386497393  1.973259302
##  [741]  3.230665825  0.362047858  0.845895659  4.760351520  0.392170457
##  [746]  1.289333679  1.390107730  0.105588347  6.773652821  1.155924348
##  [751]  0.757969513  2.128779242  0.379159184  0.623618227  3.031991624
##  [756]  0.076000754  0.807209267  1.748300163  4.461639512  1.054215336
##  [761]  0.657499920  0.210710985  1.808331951  0.443580251  3.910771010
##  [766]  3.149200957  0.203665548  2.709659614  0.289240245  0.855599562
##  [771]  3.063558448  2.248081267  1.728485268  1.545375461  1.067049000
##  [776]  0.760079646  2.213938425  1.532644812  1.949455369  1.013267063
##  [781]  3.959264181  0.498584504  0.042572682  0.607458986  3.797399413
##  [786]  1.291740315  0.648138496  1.252257912  2.014521761  0.230762992
##  [791]  3.857180361  4.076493196  2.047755994  4.721093837  0.100076211
##  [796]  0.080909591  2.972618983  5.788249820  1.233518804  2.789772611
##  [801]  1.242493241  0.120606008  0.859804978  0.118614016  0.827035046
##  [806]  4.993196111  4.309912289  0.295227075  4.530570756  3.109111711
##  [811]  1.624950084  2.479761431  0.490534487  3.355401564  0.432943977
##  [816]  1.254681486  2.395997744  1.871986760  4.607246164  1.012438751
##  [821]  7.195604150  5.809347376  0.948718289  0.688343429  3.482312667
##  [826]  0.345858924  0.300057169  1.244008121  2.981751740  0.829462889
##  [831]  2.933757689  1.230612010 11.887912720  1.329398494  0.534261900
##  [836]  0.570534741  2.756060043  1.470359697  7.390524251  4.886082981
##  [841]  1.897548117  0.022543966  3.531547334  1.641346810  1.012820049
##  [846]  0.373832142  1.944835933  0.234256156  7.172128778  1.067590000
##  [851]  2.316205619  0.133404306  2.136837063  2.259205511  2.010762480
##  [856]  2.748347843  1.660127522  1.762419607  5.736759127  1.486259431
##  [861]  2.029269779  1.363396903  1.173621806  4.419175961  0.677974001
##  [866]  0.061783839  1.338523372  0.896393698  2.628524776  0.254528407
##  [871]  1.498000547  0.072056074  6.953558098  1.006174020  0.840186022
##  [876]  1.800020505  3.308374300  1.996108750  0.140614396  2.210816066
##  [881]  0.602073169  1.310464640  0.544249735  0.039848611  1.828122284
##  [886]  2.711927501  0.948792664  1.796785369  3.466037225  3.064348859
##  [891]  1.866022281  1.854583495  1.436205437  0.715236337  1.321214749
##  [896]  0.103410034  0.080842754  1.615908826  2.030684812  0.711500848
##  [901]  0.316637640  1.001951173  1.700980078  0.336908376  0.139706890
##  [906]  2.359932959  0.244378029  3.193665046  0.038509347  5.150838438
##  [911]  0.498363663  2.414643154  4.665991703  1.224063202  0.049055069
##  [916]  1.335279658  4.614971976  0.921739902  3.207681425  0.410541642
##  [921]  0.562991014  1.989124389  5.873401649  0.750223545  1.400777947
##  [926]  1.290967501  0.398856748  1.399349194  1.016715673  2.767849142
##  [931]  0.347985761  1.604485002  0.581853715  3.716107748  0.103056557
##  [936]  1.426449111  1.370028544  0.734231736  2.220419271  0.044455830
##  [941]  1.203765598  1.654323330  0.858963675  0.816930442  1.120151298
##  [946]  0.367639421  0.673933254  0.628909214  0.378419903  0.144917897
##  [951]  0.353815993  0.084967984  0.286718429  2.598914903  1.814919569
##  [956]  0.713269352  3.080474093  0.990872624  0.952779658  0.992014452
##  [961]  2.721403662  6.898039922  1.399367244  0.890191864  0.318116514
##  [966]  0.398619546  1.945936665  2.330768816  1.979175430  1.313781413
##  [971]  4.727923866  1.422410387  2.499274669  1.010854268  0.525248797
##  [976]  0.124966842  1.802938068  0.812442408  3.271487016  1.237490395
##  [981]  1.267778101  0.220326283  0.568571589  1.305757681  1.149767489
##  [986]  1.413882373  0.041130233  0.175273127  0.969170825  0.009384243
##  [991]  3.032395328  3.172043810  0.205621679  1.260474390  1.135929230
##  [996]  1.475651914  2.255683476  2.343957718  1.054481892  0.925608196
qexp(0.75,0.5)
## [1] 2.772589
plot(1:10,pexp(1:10,0.5),type='l')

plot(1:10,dexp(1:10,0.5),type='l')

w=pexp(4,0.5)-pexp(2,0.5);w
## [1] 0.2325442
pexp(10,0.5)
## [1] 0.9932621

Gamma distribution

1-dgamma(5,2,scale=3)
## [1] 0.8950691
1-pgamma(5,2,scale=3)
## [1] 0.5036683
qgamma(0.9,2,scale=3)
## [1] 11.66916
set.seed(12345)
rgamma(100,3,2)
##   [1] 1.7557567 1.8737999 1.1650815 1.2683480 3.7522476 2.0990317 1.0354453
##   [8] 2.9081868 0.9203033 1.5601777 1.6950954 0.7270646 2.2071692 2.2930008
##  [15] 1.4973163 1.9423215 2.6658129 0.7925085 0.2629451 3.0843520 0.8982223
##  [22] 1.2484964 1.1249750 0.7905719 3.3949248 2.8736714 1.4591008 1.6684767
##  [29] 1.0069161 1.5007742 1.5851129 0.5651256 4.7770212 1.7535638 0.4303502
##  [36] 1.4969288 1.4991032 2.4844752 2.2707159 0.7040824 1.8561336 1.9860972
##  [43] 3.5209858 5.1385506 1.6819516 1.5259868 3.0040404 1.2429538 2.1062534
##  [50] 1.9885524 0.6907457 1.1182759 1.8122850 2.2106959 1.0209552 0.6183555
##  [57] 3.1618289 1.8377514 1.0183959 2.6121545 2.1143922 1.0765061 3.1868336
##  [64] 0.9594299 0.5802978 0.8826117 2.4144037 1.3975815 1.6900162 1.2830486
##  [71] 2.5922330 1.0213365 2.5129790 1.5176559 2.7533042 0.9391611 3.0048486
##  [78] 0.7925240 5.0941917 1.2871922 2.1247476 0.9392470 2.0587156 1.3620493
##  [85] 0.2975866 1.5814457 1.6427481 0.7480035 1.0594811 0.7186560 1.3041527
##  [92] 0.7885846 1.6291049 1.0643711 0.8981646 0.7326426 1.8005330 0.4619812
##  [99] 1.7805549 2.3566973
plot(1:5,dgamma(1:5,2,3),type='h')

Normal distribution

dnorm(550,544,103)
## [1] 0.00386666
plot(1:550,dnorm(1:550,544,103),type='h')

pnorm(480,544,103)
## [1] 0.2671816
pnorm(460,544,103,lower.tail=F)
## [1] 0.7926166
w=pnorm(730,544,103)-pnorm(480,544,103);w
## [1] 0.6973455
qnorm(0.8,544,103)
## [1] 630.687
rnorm(100,544,103)
##   [1] 596.3426 645.5256 577.2499 707.5246 614.6056 576.1082 579.7268 606.3264
##   [9] 563.5509 626.0017 445.0379 472.0914 603.2130 475.8209 562.5558 625.1268
##  [17] 575.9207 526.9846 746.0737 532.9202 634.8152 591.6136 655.3476 453.0167
##  [25] 353.3642 652.7158 444.9022 457.0791 512.7003 426.0156 537.3819 468.1516
##  [33] 441.1150 470.4048 398.2208 603.1002 343.1714 620.1518 514.7295 424.2474
##  [41] 480.0591 474.9484 647.9643 491.8501 576.2601 380.1137 493.1720 561.4596
##  [49] 662.9200 417.3693 634.0736 593.1566 677.8313 272.9872 733.2671 517.9163
##  [57] 639.3144 596.9075 476.4510 407.0994 691.8472 655.7768 517.2331 511.5542
##  [65] 487.6889 522.4126 581.0623 493.7092 622.0347 421.2116 479.1099 552.7428
##  [73] 582.0636 658.2177 675.7206 636.5479 567.3841 498.9696 615.8834 660.6349
##  [81] 618.8310 699.2464 654.7921 579.6843 612.7375 510.2868 590.1097 593.3605
##  [89] 473.3773 625.4233 455.9069 568.8707 489.6666 563.1437 634.2524 505.9804
##  [97] 584.3240 639.5398 685.5743 519.5346

Weibull distribution

dweibull(3.5,shape=2,scale=3)
## [1] 0.1994034
pweibull(3,shape=2,scale=3,lower.tail=F)
## [1] 0.3678794
w=pweibull(6,shape=2,scale=3)-pweibull(1.8,shape=2,scale=3);w
## [1] 0.6793607
qweibull(0.40,shape=2,scale=3)
## [1] 2.144162
rweibull(1000,shape=2,scale=3)
##    [1] 3.20225147 3.57680342 2.36396161 1.72679629 2.36238634 6.04276652
##    [7] 2.06387067 2.13395244 1.55563141 1.09937266 2.70525226 2.47643251
##   [13] 1.01995446 2.96054342 3.49285634 3.99685295 4.69438875 1.85579892
##   [19] 3.03768367 4.95944929 4.92011039 2.26593550 1.85565703 3.85439709
##   [25] 3.45409199 0.71715269 2.42729968 1.64229681 3.68289595 2.00557141
##   [31] 2.05213609 2.35217424 3.57919003 3.53348849 2.61505574 1.27606711
##   [37] 3.61593309 1.51408265 2.42021990 3.14063043 1.50129782 3.59626257
##   [43] 3.12990897 2.77695927 1.79841406 1.95012078 1.71210458 4.03321910
##   [49] 5.18120285 2.23909643 4.41942320 6.11142194 1.50598761 3.44909482
##   [55] 1.86231468 3.68042101 0.48461723 1.86735953 1.48908789 1.79431168
##   [61] 6.40995441 2.48360031 1.67909125 3.15974993 1.33438439 1.04939303
##   [67] 1.18307184 2.66869141 2.60536397 2.44297068 4.03480396 1.05380911
##   [73] 3.80211313 2.02321375 5.29729425 2.98709886 2.13075517 0.66091171
##   [79] 3.72021598 3.93300716 1.13346590 2.62510426 3.65340004 0.93924046
##   [85] 0.50471312 0.61949321 2.32773668 0.37234057 3.08001133 2.96665387
##   [91] 2.79307923 3.37240069 4.93885366 4.77001610 2.74544043 0.32501901
##   [97] 4.42988391 3.68929981 3.68975489 1.97554425 2.46430641 1.69228147
##  [103] 3.22019073 1.22658106 2.47551888 1.85386029 0.71739100 6.17726842
##  [109] 2.42210930 1.31729999 3.16721936 1.85323631 2.08211071 1.96256537
##  [115] 0.63470768 3.61810417 3.16015330 1.26090636 4.16860622 0.85049076
##  [121] 4.68908604 1.84147492 0.54401356 2.01626243 2.79221604 1.39665851
##  [127] 3.47997977 1.94397034 2.20524096 1.99288600 5.75547591 4.96889311
##  [133] 0.41719680 0.75004744 3.82323368 1.82237832 3.15952948 1.87173176
##  [139] 4.85681087 0.41455755 4.31723343 2.95429143 1.19492952 1.29687911
##  [145] 1.89541407 1.78121832 1.05063743 2.63645300 1.79061823 2.70503486
##  [151] 0.92062085 4.38214766 5.09673655 1.76566119 1.12647318 6.91678097
##  [157] 1.57833477 1.48772544 2.52015556 2.09094120 3.04854061 2.62349378
##  [163] 3.29659320 4.87553722 1.71055424 4.21140942 1.49606578 1.18777372
##  [169] 3.09716585 3.03517507 0.75553999 2.01447654 3.12196028 2.45717066
##  [175] 2.72891101 1.85626241 0.93169377 3.93483889 3.46042432 3.05912291
##  [181] 5.60862117 5.49454352 4.64419237 2.09674719 5.94498101 2.77582050
##  [187] 4.76487993 2.47204028 2.37239326 1.63771281 2.00533738 2.06784737
##  [193] 1.17080466 0.66267895 2.06593901 1.61130283 4.41344483 2.90835697
##  [199] 0.87888831 2.71090778 4.94075966 0.63955800 0.72291086 1.85840658
##  [205] 5.10863472 1.72085511 3.16753750 1.61913073 0.74128581 3.70250885
##  [211] 1.63786012 1.08376887 2.66099273 5.77030041 3.43796339 1.49883177
##  [217] 1.74257240 0.32848674 6.05447464 3.21737418 3.51145902 2.64678012
##  [223] 2.37705801 1.99072458 0.85145337 3.30926514 1.36813310 1.81393641
##  [229] 3.86041881 2.71762776 1.16602317 1.34844692 3.23521451 0.33618801
##  [235] 2.90349867 4.40295037 6.02925409 3.12540824 1.31390070 1.46576044
##  [241] 2.96857190 1.82452772 2.11669484 2.32812173 1.17437199 3.04579814
##  [247] 3.26701685 2.13203582 3.17369678 2.13153293 3.53868018 1.64931592
##  [253] 6.14434946 2.07206069 1.15523868 2.54546296 2.54141248 4.71464964
##  [259] 2.87698968 1.66467028 0.69752205 2.49458256 5.47293682 2.10240247
##  [265] 4.45082231 4.07352749 4.08172377 3.43986317 3.36668475 1.43210356
##  [271] 2.66583902 2.62072723 2.21386921 3.15067589 1.58439326 4.41967000
##  [277] 0.77071919 4.10544656 2.36234137 4.02209643 2.10663029 2.73301101
##  [283] 1.61732128 1.04450536 4.22092147 2.40243365 1.77449668 3.87366585
##  [289] 5.14681947 2.52636238 1.99137006 2.04427288 2.57607181 3.95401985
##  [295] 2.75517840 4.29367633 1.84398902 1.15917723 2.30895846 1.80436190
##  [301] 3.39319938 2.09063628 2.44194279 3.35255634 2.48169765 2.20698389
##  [307] 4.01533373 1.02267375 2.50757425 3.14332557 0.64839210 0.92903184
##  [313] 3.25734712 3.67686082 3.28345908 1.01874391 2.07498878 1.68752235
##  [319] 2.10877209 3.77436486 4.61334350 2.56652001 1.38115586 2.25709642
##  [325] 1.92872900 4.45455604 4.87554341 1.96640162 0.87111088 1.83398031
##  [331] 3.82655364 0.33746433 2.44821696 1.36150561 2.74439808 1.46499029
##  [337] 6.09529339 0.49134625 4.04224603 1.95740792 3.08408487 1.65918548
##  [343] 2.83072736 2.35189622 1.68496689 1.23633619 2.97982844 1.03514686
##  [349] 5.79203693 1.82113419 4.04043019 3.91866547 4.58248798 6.19810396
##  [355] 3.92246116 1.90025173 3.25714169 4.12020290 3.46813852 1.56367588
##  [361] 4.37110462 1.21775833 3.16360161 3.36527717 5.15004247 3.14956496
##  [367] 2.28391024 1.24139733 4.00135593 1.04557834 3.97154281 0.79188020
##  [373] 1.64107972 2.72659774 1.53331632 3.96305912 3.12215382 2.01191875
##  [379] 3.12046479 4.56032768 1.75332815 2.90076654 2.32010634 2.27613122
##  [385] 3.38842768 3.87259332 4.62098075 2.67522319 1.22242286 3.82848566
##  [391] 1.98443680 4.08018958 1.09111616 3.92615059 2.12005553 5.97863555
##  [397] 3.06344569 2.70293717 2.17265337 0.95756211 2.07711624 2.54001967
##  [403] 1.32996226 6.27112015 0.89875792 1.76601848 2.26648435 1.42914671
##  [409] 2.28768301 3.24936356 3.12130541 3.41387940 3.61284592 3.27245533
##  [415] 2.53108735 2.50475818 3.97419655 2.63880145 3.12277429 2.53230752
##  [421] 2.43732375 2.68333098 1.92131592 2.68997340 2.46029470 1.88081868
##  [427] 2.82782611 4.76997998 1.54618095 2.20180485 0.87784714 1.51814776
##  [433] 0.79906606 2.30186918 1.98310637 2.27230165 2.84882202 2.17793872
##  [439] 0.90728670 4.34739436 2.68934510 1.40269316 0.73842699 2.85468117
##  [445] 3.04946735 5.86441168 1.63913521 2.83295337 5.81145804 2.18374434
##  [451] 3.44462826 3.63360338 2.37500568 3.81433501 1.15838780 2.65983870
##  [457] 3.66950694 2.96033296 4.25434777 4.79453174 1.23672110 6.70070149
##  [463] 3.06887594 1.84149347 3.51151319 3.96630981 1.76609203 0.06243938
##  [469] 0.68169633 2.73603323 1.01615482 2.18880471 3.09972486 1.37897662
##  [475] 2.34894258 6.10893460 1.65477571 2.84208789 1.58073929 5.83236453
##  [481] 4.09817947 4.47131818 3.38181096 1.41194379 1.19914673 2.56484459
##  [487] 1.53224257 1.94522450 2.43542081 1.50079498 1.81813441 1.38897480
##  [493] 3.72359213 4.50555090 3.69924481 2.72838009 5.30619876 3.27264349
##  [499] 1.69496380 1.93309414 3.60787953 1.74227020 1.23685864 1.54853911
##  [505] 1.44277274 3.12008112 3.22759908 2.43811904 2.48015330 2.18357791
##  [511] 0.50343615 1.47918234 2.00163064 3.13295194 4.67034186 3.04630976
##  [517] 2.48023299 5.41180493 2.65112463 2.76672727 0.43358509 1.42465250
##  [523] 2.98300760 3.39174282 5.09035808 3.03303340 1.97769510 0.39575772
##  [529] 0.43140610 1.64371710 5.58007192 2.96143176 2.75820983 1.06266365
##  [535] 1.94117805 1.75516828 2.71201331 2.57539466 4.91818598 0.38921091
##  [541] 1.55648714 2.77295582 3.91570365 2.35728018 4.42112384 0.50595125
##  [547] 4.67619254 0.69640134 6.28993657 0.40626110 1.27545095 3.56100277
##  [553] 2.22800724 6.36503527 2.01155271 5.21167629 2.88991278 1.73580789
##  [559] 8.25401709 3.20786390 1.39338859 2.54557919 2.75116112 1.97939162
##  [565] 1.66798012 1.08915568 1.50718372 0.87167697 3.22249307 0.39360083
##  [571] 2.21575152 4.21869313 4.90005712 1.03388153 1.33929996 1.60584021
##  [577] 4.57906075 3.61655278 2.58280311 2.33751989 3.94145302 2.40460400
##  [583] 1.98641244 3.46141746 2.84282210 1.79859193 3.84242735 3.74204879
##  [589] 1.06777682 3.54378743 1.65952210 2.55130591 3.33608315 2.92320226
##  [595] 2.98631394 4.11447372 2.53657352 0.87192205 1.28797222 1.42262718
##  [601] 4.77840791 2.98836219 2.40835906 1.77871349 2.52755898 4.42383469
##  [607] 3.52193454 1.66370397 2.54086159 1.72763703 2.36427173 1.01513356
##  [613] 2.14624454 1.85310423 2.69912957 5.01843143 2.33954433 2.41842169
##  [619] 2.68648028 1.60248387 0.24005180 4.67175012 5.00342671 2.15531586
##  [625] 3.94432287 2.95382976 3.42838906 1.54238495 1.12969294 2.21486995
##  [631] 0.43250067 5.06873042 3.44356336 2.46391488 2.74261385 1.46193010
##  [637] 4.59476190 6.86736699 1.13658781 3.29574864 1.46004584 4.60667228
##  [643] 0.29070796 1.46281078 1.23961681 1.56364942 3.15083930 1.21402576
##  [649] 1.81692654 0.65321001 1.16816144 2.83087488 1.03869784 2.78825137
##  [655] 1.46228118 1.20200280 3.83313978 3.16164377 3.52766697 5.17775718
##  [661] 1.40427544 2.20094155 2.19496236 3.19782725 0.61809345 3.51259951
##  [667] 3.68280315 2.69155239 1.65575292 4.62206315 3.42823841 2.38836719
##  [673] 2.10255749 3.07331422 0.55164976 1.30225493 1.80383664 2.46656447
##  [679] 4.03802903 3.18757050 4.10595715 2.17735813 1.75035674 4.75257178
##  [685] 2.15100893 1.32683236 3.52980246 2.40318433 5.18477171 1.46051921
##  [691] 1.82926125 2.58525063 1.25948528 2.37054493 2.16238872 1.94824535
##  [697] 3.57626533 3.88382076 2.92623069 0.82974756 5.11202665 2.20921708
##  [703] 1.78519792 2.57883692 1.36644950 3.47628591 4.86668896 1.55818639
##  [709] 1.13617641 2.59104305 0.47184087 2.31015620 2.59524089 2.44795336
##  [715] 3.27164429 2.10605573 3.62930606 1.33222213 1.15044074 4.14273027
##  [721] 2.31636570 2.81179174 2.24113126 0.58814955 2.08405462 0.82016187
##  [727] 4.18240622 3.04170312 3.32493502 3.43334086 1.54602927 1.82737884
##  [733] 2.66518479 2.15458979 2.01273625 2.68409087 1.79122160 4.49838515
##  [739] 3.20059408 0.68701998 1.67961005 1.27254790 3.81083911 1.16132388
##  [745] 2.47183321 3.03373500 0.61092794 4.09671692 5.59898123 0.92586986
##  [751] 1.65139992 2.72505851 3.87190676 1.32434953 1.92663873 1.36473579
##  [757] 3.16515201 2.29249998 3.84909405 3.76793763 3.14723605 4.47484633
##  [763] 2.85002013 0.30444562 2.40808773 2.42516048 3.57763073 2.09375602
##  [769] 4.17412121 5.49175100 1.38365842 4.31717230 1.37461496 0.97439028
##  [775] 2.66701284 4.68793600 1.73777684 0.52106287 0.64639117 4.70389561
##  [781] 2.21446210 1.76736894 4.67069875 4.47693219 4.46679379 0.52578755
##  [787] 2.23588086 4.83933951 4.16116849 2.72179905 2.49327678 3.97923455
##  [793] 2.92426768 2.06498745 4.05134385 2.11535598 1.36227732 2.96620972
##  [799] 2.56396313 3.07234867 2.50344026 4.80966174 0.47917686 1.28519474
##  [805] 0.74091477 1.68179966 5.63287614 3.04788611 3.86282970 5.48407456
##  [811] 1.01750909 0.90855677 1.84756562 1.89111677 3.56786354 2.26522505
##  [817] 0.71981609 2.45471405 1.07183576 3.53485887 0.59461001 1.11011769
##  [823] 3.71130013 0.36916844 1.37308503 4.22134754 1.76518190 4.24469730
##  [829] 1.00454248 0.95488925 1.03542446 7.28865727 1.28511647 2.02670357
##  [835] 1.08415254 2.82671882 1.98125819 2.78951339 2.72385823 0.68777951
##  [841] 5.02246524 5.59745155 2.11947199 2.86676236 3.15389056 4.70766869
##  [847] 3.22923128 0.82803859 2.69317145 6.08853831 3.97738845 3.37585764
##  [853] 1.59711003 2.16704845 3.20312930 1.14563962 4.00022112 1.74593320
##  [859] 6.03385038 0.31001207 1.53332136 0.44378677 1.19139950 2.58139649
##  [865] 1.32557829 1.89570657 1.20442353 4.59010307 3.09348708 2.54849154
##  [871] 2.34996530 1.32687519 0.42078194 3.03595804 2.59303305 1.86372025
##  [877] 2.67906763 2.79320719 2.62508284 2.50535539 3.82058041 3.30540979
##  [883] 5.12162080 3.27754448 4.22038831 2.62086230 4.86478349 1.90360091
##  [889] 3.15718638 1.24903412 1.44318679 4.34808998 3.87985036 0.65385100
##  [895] 3.66372130 1.03286694 0.69138176 2.53722789 1.05118652 2.92970976
##  [901] 5.29119358 1.27549669 1.70453852 2.85107356 0.76862518 3.90573857
##  [907] 3.31371180 3.46229804 1.04834267 5.15873087 0.45436016 6.10991851
##  [913] 1.60332019 0.39649966 1.57350811 2.12294511 1.37372754 3.28396541
##  [919] 4.07170323 2.52032213 0.58828960 2.71866036 1.30928883 2.37209048
##  [925] 2.59095768 1.48772262 2.16246957 1.96719921 1.30493382 2.01795119
##  [931] 1.10068080 5.65187738 1.68390468 2.58111101 1.94875734 3.20799337
##  [937] 2.81069977 1.65652856 3.28580275 4.00448466 3.64987251 3.74514589
##  [943] 3.40899135 3.24678830 2.72930598 3.12533720 1.05116144 3.50068652
##  [949] 1.86728098 0.87434518 0.65783291 0.09433967 2.40512174 0.51159643
##  [955] 5.05736613 3.08932860 2.57954955 3.39094614 3.15642339 1.87059577
##  [961] 1.20400939 2.35945652 3.64550183 1.60726072 2.70693200 3.65312689
##  [967] 2.54543964 1.22054270 0.28038221 3.56808166 0.29463022 4.54462172
##  [973] 3.48649054 2.63187050 2.98444249 0.54393963 3.75230364 3.95234853
##  [979] 2.59590552 4.12254638 2.46306309 4.61825496 2.05813639 2.61982989
##  [985] 1.63954833 1.49342534 4.46120312 2.73157480 3.00848448 1.39315017
##  [991] 2.45361785 1.27892160 4.80671315 1.68137907 4.11624040 0.23780726
##  [997] 3.30941227 1.09151733 2.34414396 0.52715575
set.seed(1457)

Uniform distribution

dunif(7,min=7,max=10)
## [1] 0.3333333
punif(8,min=7,max=10,lower.tail=F)
## [1] 0.6666667
qunif(0.6,min=7,max=10)
## [1] 8.8
w=punif(9,min=7,max=10)-punif(7,min=7,max=10);w
## [1] 0.6666667
runif(1000,min=7,max=10)
##    [1] 9.193103 8.858801 8.687552 7.678559 8.771969 7.456392 8.927428 8.160849
##    [9] 9.413554 7.662419 9.207941 7.630169 7.567214 7.053775 8.043641 8.503577
##   [17] 8.183512 8.871886 7.200354 9.054497 7.283783 8.067874 8.492236 9.127791
##   [25] 8.443669 7.646573 9.103155 9.775478 7.664123 8.189467 9.710129 7.422936
##   [33] 7.335830 7.825547 7.344703 9.081442 9.368146 7.573699 8.622228 8.129202
##   [41] 9.319774 8.524195 7.591252 7.347907 7.574011 7.724834 8.853938 9.753024
##   [49] 7.626638 8.510582 7.563760 8.430988 9.897150 7.919033 9.863138 7.363631
##   [57] 7.979877 7.025516 9.721008 9.078180 7.995701 7.935457 8.150734 7.925264
##   [65] 8.305099 9.595648 9.839234 9.343780 9.164669 8.156929 9.389275 7.175311
##   [73] 7.552130 8.843130 7.775515 9.430365 7.647342 9.924123 8.329472 7.117501
##   [81] 8.022095 7.019218 8.081712 7.316975 9.080064 8.674268 9.032426 9.324072
##   [89] 7.274723 9.185607 8.695076 8.557913 8.963560 7.562247 7.366256 8.793000
##   [97] 7.601157 9.624534 8.493029 8.690233 9.442141 9.106069 9.028975 9.688192
##  [105] 9.434578 9.185125 8.330231 9.607723 7.025214 8.853226 7.052478 9.290095
##  [113] 8.018914 9.359650 8.417860 8.123806 8.259002 9.472530 9.019492 7.133659
##  [121] 7.917441 8.651172 8.612991 8.849117 8.333857 9.349350 8.574664 9.177327
##  [129] 9.306159 9.204843 9.504094 7.096320 8.640428 8.312740 8.386061 8.153041
##  [137] 9.110388 9.414962 9.191078 9.631791 8.023779 8.049791 7.168393 9.153329
##  [145] 9.840285 7.805418 9.667299 9.921357 7.457843 8.193562 7.297992 9.725168
##  [153] 9.443203 8.689497 9.936866 9.829749 7.483452 9.051967 8.518925 8.894798
##  [161] 8.658942 7.637741 8.110721 7.028981 7.119606 7.520273 7.102404 8.524763
##  [169] 9.834084 8.893481 7.664625 7.203717 8.508155 8.684292 7.130102 8.882860
##  [177] 9.581425 8.292373 8.181881 9.741770 7.757735 9.388052 7.225327 9.222324
##  [185] 8.269875 8.719746 9.867445 9.957276 7.586627 9.227774 7.313069 9.311484
##  [193] 9.580868 8.361095 8.358315 9.094625 7.094569 8.051521 8.956916 7.638783
##  [201] 8.918131 8.624801 9.623369 7.931257 7.048622 9.091598 9.761619 8.965039
##  [209] 7.550006 7.031854 9.911447 7.542431 7.162928 7.004928 7.542018 9.792259
##  [217] 9.024125 9.716963 8.188101 9.908243 9.002653 7.056090 9.580539 7.391601
##  [225] 9.598420 9.629039 8.978674 9.052975 8.787466 7.539188 7.205568 7.727185
##  [233] 7.130020 8.389901 8.995293 9.837408 7.243408 7.050002 9.223448 9.431604
##  [241] 8.789422 9.589919 7.898557 9.900414 7.569258 9.392550 8.633118 9.888885
##  [249] 7.361702 9.448969 7.138412 9.512275 9.254303 7.184565 9.569830 7.596424
##  [257] 9.917990 8.019353 9.483373 9.212918 9.755253 7.985257 9.035185 7.967645
##  [265] 8.125511 7.712651 9.077328 9.598976 8.449807 9.465045 9.458872 7.216347
##  [273] 9.704148 8.513081 7.870513 7.634062 9.036627 7.746619 9.605976 8.753504
##  [281] 8.442178 8.001018 7.122221 7.485451 7.172473 8.746564 9.492743 9.643073
##  [289] 8.048258 9.574763 9.311142 7.763317 9.142798 9.627837 7.559393 8.274982
##  [297] 9.987302 7.745358 7.260957 9.232433 9.797075 9.626818 8.640489 7.057909
##  [305] 9.633246 7.693614 9.994073 9.475296 8.397461 8.880689 7.659034 9.317966
##  [313] 8.973822 9.326267 7.719732 7.314812 9.274011 7.826732 9.428984 7.680444
##  [321] 9.853787 8.630079 7.970615 9.372492 9.868328 9.946525 8.582794 8.665712
##  [329] 9.766252 9.736710 7.534549 7.557217 8.499563 9.380598 7.234395 7.687131
##  [337] 8.792380 7.746030 9.320455 9.289949 9.777911 8.240176 8.791048 8.108074
##  [345] 8.399096 9.487246 8.728111 9.237976 8.886258 8.997519 9.673275 7.826182
##  [353] 7.438678 7.193922 9.822335 7.081852 9.128762 8.612089 7.748257 8.264758
##  [361] 7.823698 9.885003 8.233647 9.795073 7.276936 9.722262 8.377305 7.536112
##  [369] 9.086424 9.880477 7.285291 7.595384 7.410118 9.186767 9.573410 7.612953
##  [377] 8.715185 9.942331 9.481633 8.913368 7.426234 7.379032 8.618045 8.265529
##  [385] 7.190609 9.676070 9.021728 9.680318 9.772114 9.358428 7.499168 8.307174
##  [393] 8.709231 9.300894 8.100781 7.301144 9.703919 7.695359 7.028953 9.648571
##  [401] 8.598476 9.507553 8.906374 7.265892 7.567404 7.354919 7.783631 8.163605
##  [409] 9.303171 9.892929 7.726299 9.619693 8.150603 7.493321 9.471646 7.842139
##  [417] 8.458406 8.862484 9.547724 9.998499 8.992744 9.601610 7.004733 9.860283
##  [425] 7.377392 7.895353 8.054155 8.379472 8.286028 7.680677 8.009949 9.387729
##  [433] 7.949347 9.019212 9.453846 7.144344 7.929869 7.990734 8.927226 7.835840
##  [441] 9.195281 8.364719 7.070308 9.391776 9.463822 8.738143 9.894758 7.476971
##  [449] 9.266430 9.141240 9.973699 9.668844 9.622179 9.915712 9.167239 7.168677
##  [457] 7.167320 9.114301 9.524402 7.924049 9.844374 8.879939 9.275910 8.714404
##  [465] 7.052949 7.871757 7.185918 9.432257 9.308058 9.415164 8.222499 7.977407
##  [473] 7.695046 7.483666 9.176759 7.413292 9.429638 9.269381 9.210024 9.153298
##  [481] 8.625641 7.197281 8.968702 9.396833 7.992716 9.347520 7.296494 8.681321
##  [489] 9.178258 8.255590 8.299798 9.799725 8.547626 7.621141 7.792126 7.701645
##  [497] 7.248530 9.103850 8.373212 7.658297 8.727300 9.041336 8.179433 7.456985
##  [505] 9.005507 9.589780 7.502577 9.257558 8.703665 9.490168 7.946920 9.232708
##  [513] 8.927597 9.575753 7.883175 8.580668 7.998157 9.657847 9.749245 8.001311
##  [521] 7.217108 9.515021 7.762202 9.445068 9.446359 8.589237 9.613929 8.110725
##  [529] 8.477882 8.949006 9.687884 9.795354 7.888422 8.292586 7.247059 8.270922
##  [537] 7.306278 9.892584 7.993607 8.816281 7.460336 8.839668 7.559373 7.987072
##  [545] 8.670226 9.799890 9.123613 8.423216 9.681571 9.543204 7.693983 8.171310
##  [553] 8.553902 9.143500 8.815609 7.445617 7.535142 8.985834 8.062338 7.658547
##  [561] 7.158698 8.184417 9.523570 9.964143 8.509738 8.942102 9.598556 7.355600
##  [569] 8.867554 7.973016 7.741439 8.323254 9.253502 7.170163 7.722416 7.369690
##  [577] 7.742532 8.282684 8.189571 9.756296 7.435343 7.231683 8.726620 7.793181
##  [585] 7.560136 8.519481 9.999805 9.651928 8.890118 8.223632 9.276471 7.925048
##  [593] 7.778105 9.297469 9.362195 7.270772 7.347410 9.348395 9.938620 9.488974
##  [601] 7.982128 9.251860 9.195621 7.545181 9.475545 9.529650 7.274387 7.226990
##  [609] 9.584920 9.366389 8.906626 9.109869 7.717780 9.267238 8.738174 8.189544
##  [617] 8.083476 7.597843 7.415076 9.940981 9.591383 9.685053 9.679993 9.260689
##  [625] 7.237063 8.891871 9.240728 7.082265 8.112956 8.183132 7.514380 9.709352
##  [633] 9.461099 7.946849 9.220671 8.016297 7.688620 8.261326 8.973989 7.061383
##  [641] 7.256337 7.179242 7.237369 8.329681 7.709947 9.394772 7.549784 8.445682
##  [649] 8.187877 9.105495 8.015746 8.313711 9.394911 7.454548 7.848326 7.802116
##  [657] 7.904543 7.410833 7.695169 8.861874 7.524117 8.670658 8.026385 7.964357
##  [665] 7.131247 9.746345 7.489414 9.661104 8.415095 9.567468 9.426974 8.281575
##  [673] 8.410696 9.869173 8.519619 7.110028 9.489721 9.099770 7.792045 7.547348
##  [681] 7.377779 9.669076 8.961700 7.527537 7.210878 7.675214 8.616694 7.540649
##  [689] 8.062016 7.685236 9.757837 7.698809 9.073348 7.745062 8.741549 9.577690
##  [697] 9.854203 9.836124 8.870859 8.278655 7.369433 7.980270 7.288649 8.170523
##  [705] 8.024339 8.337947 8.678656 9.887555 7.525334 9.373743 7.437972 7.525623
##  [713] 9.549254 7.998365 7.203092 7.051515 8.792109 7.169449 9.162042 7.532913
##  [721] 9.885011 8.323798 8.712496 8.124097 8.915293 8.972115 7.268457 7.775344
##  [729] 7.366772 7.337443 9.510395 8.349767 9.571856 8.493542 8.215178 9.161328
##  [737] 7.241880 7.069370 7.180674 9.341425 9.112260 9.696333 9.715165 9.924947
##  [745] 7.431812 8.058413 9.569917 8.458255 9.365840 7.055943 7.155750 7.017858
##  [753] 9.969032 9.463914 9.482412 9.185618 8.042816 7.700821 9.609024 9.409366
##  [761] 9.969923 9.641026 8.176351 9.759598 7.817533 7.459993 7.790396 9.790276
##  [769] 7.548032 8.725292 8.082411 9.738417 9.599584 8.014206 9.708814 8.981355
##  [777] 8.185244 7.975917 8.148790 8.871092 9.468870 8.090310 8.227885 9.456570
##  [785] 9.054554 8.813039 8.593785 9.392419 9.948389 7.811420 8.402356 7.131228
##  [793] 9.242884 9.976849 9.343982 8.454934 7.954470 8.375069 9.170035 7.465265
##  [801] 8.090562 9.792696 9.271523 9.563025 9.914285 9.540352 9.543783 7.650510
##  [809] 9.836707 8.912703 9.278082 7.289950 7.852586 9.005148 8.152405 8.117086
##  [817] 8.904920 8.650947 9.492076 7.242920 7.429478 7.454334 9.924163 8.632152
##  [825] 9.499064 7.892053 9.357890 9.155619 8.033854 7.863527 8.672056 8.511910
##  [833] 7.841336 7.228358 8.993937 9.344734 8.918705 8.955865 9.876929 8.343463
##  [841] 7.462816 7.961100 9.231067 7.760997 9.119273 9.559181 8.928374 8.955414
##  [849] 8.556225 8.813172 8.556330 8.335902 7.979692 9.593528 7.776726 8.126492
##  [857] 9.556550 8.490162 9.840510 7.811578 8.839122 8.327549 7.803774 9.429590
##  [865] 8.048039 8.125948 7.205801 9.020628 8.369707 8.242099 9.756990 9.457029
##  [873] 9.467419 8.248776 9.606870 9.518733 7.968658 9.632052 9.957833 9.303138
##  [881] 7.301288 8.127423 9.687705 9.398489 7.550195 8.631469 7.273076 7.868336
##  [889] 8.003196 8.344002 8.315339 7.672312 9.860672 9.010103 8.963519 7.675792
##  [897] 7.196930 7.718248 7.675511 9.755439 8.579990 8.216350 8.510591 9.130326
##  [905] 9.043574 9.024451 8.292512 8.252319 9.819408 9.866608 7.532703 7.345759
##  [913] 8.414461 9.577829 7.449871 8.784694 7.200490 7.910656 9.097561 7.329667
##  [921] 9.103623 9.925958 8.253817 8.009575 9.260893 9.958633 7.753410 8.916128
##  [929] 7.355330 9.507705 8.853286 9.779349 7.298028 8.443005 7.432662 9.168677
##  [937] 8.186615 7.636060 7.301561 8.884294 8.361421 8.366621 7.952749 8.997992
##  [945] 8.506836 9.434161 7.217683 7.045039 8.052772 8.732242 7.336290 8.973534
##  [953] 8.859368 7.035204 9.821818 7.450262 9.215429 9.441457 8.249436 9.022579
##  [961] 7.759393 9.203456 9.572614 7.742809 8.609370 7.348998 8.865857 9.896203
##  [969] 9.636330 8.448143 7.665904 7.217973 7.775880 7.148895 9.583165 8.827671
##  [977] 7.124790 7.276778 7.687397 7.436142 9.503477 7.844571 9.158236 9.034363
##  [985] 8.735950 8.128374 8.082733 9.960908 7.024830 7.824850 9.041193 8.949170
##  [993] 8.474350 9.696550 8.299212 8.382826 7.162277 7.057986 8.736105 7.666453

Hyper geometric distribution

dhyper(0,5,11,4)
## [1] 0.1813187
plot(0:4,dhyper(0:4,5,11,4),type='h')

phyper(1,5,11,4)
## [1] 0.6346154
1-phyper(1,5,11,4)
## [1] 0.3653846
w=phyper(4,5,11,4)-phyper(1,5,11,4);w
## [1] 0.3653846
plot(0:4,phyper(0:4,5,11,4),type='s')

qhyper(0.90,5,11,4)
## [1] 2
rhyper(100,5,11,4)
##   [1] 2 2 2 1 1 0 1 1 2 0 2 1 2 1 0 2 1 1 1 1 1 2 2 3 0 1 1 2 1 1 1 2 2 2 1 1 2
##  [38] 2 1 1 2 0 1 0 1 0 0 1 1 3 0 1 1 1 0 0 0 0 2 1 3 0 1 1 1 2 1 0 1 3 2 2 1 1
##  [75] 0 1 1 1 2 1 1 0 0 2 1 1 0 1 0 0 0 1 1 0 1 1 1 1 2 1
set.seed(12345)

Binormal distribution

dbinom(5,10,0.4)
## [1] 0.2006581
1-pbinom(4,10,0.4)
## [1] 0.3668967
qbinom(0.7,5,0.4)
## [1] 3
rbinom(100,10,0.4)
##   [1] 5 6 5 6 4 2 3 4 5 8 1 2 5 0 4 4 4 4 3 7 4 3 7 5 5 4 5 4 3 4 5 0 3 5 3 3 6
##  [38] 6 4 2 5 4 6 5 3 3 2 1 2 4 7 5 3 3 5 4 5 2 4 3 5 3 7 5 7 3 7 2 4 7 5 4 3 3
##  [75] 2 4 7 5 4 2 6 4 1 1 2 3 5 4 5 2 6 5 2 4 5 4 5 5 2 4
plot(1:10,dbinom(1:10,10,0.4),type='h')

Geometric disribution

dgeom(10,0.3)
## [1] 0.008474257
1-pgeom(5,0.3)
## [1] 0.117649
qgeom(0.83,0.3)
## [1] 4
plot(1:10,pgeom(1:10, 0.3), type='h')

rgeom(100,0.3)
##   [1] 2 1 0 4 4 0 2 0 1 3 3 0 2 2 0 1 0 0 2 4 1 1 2 4 1 1 1 0 2 0 2 5 1 0 2 9 0
##  [38] 0 5 0 0 4 2 2 8 2 1 0 1 1 2 1 2 0 0 0 0 2 4 0 5 0 1 0 0 7 1 1 0 0 4 3 1 1
##  [75] 1 0 3 1 0 1 2 0 5 0 7 2 1 1 0 3 1 1 0 0 4 2 1 0 1 2
w=pgeom(10,0.3)-pgeom(5,0.3);w
## [1] 0.09787573

Chi-square distribution

dchisq(10,df=8)
## [1] 0.07018695
pchisq(12,df=8)
## [1] 0.8487961
qchisq(0.05,df=8)
## [1] 2.732637
set.seed(12345)
rchisq(5,df=8)
## [1]  9.362270  9.906250  6.596998  7.086790 18.351175
plot(1:10, pchisq(1:10, df=8),type='s')

Binomal distribution

dbinom(5,10,0.4)
## [1] 0.2006581
1-pbinom(3,10,0.4)
## [1] 0.6177194
w=pbinom(8,10,0.4)-pbinom(5,10,0.4);w
## [1] 0.1645609
plot(1:12, pbinom(1:12, 10, 0.4),type='s')

set.seed(12345)
rbinom(100,10,0.4)
##   [1] 5 6 5 6 4 2 3 4 5 8 1 2 5 0 4 4 4 4 3 7 4 3 7 5 5 4 5 4 3 4 5 0 3 5 3 3 6
##  [38] 6 4 2 5 4 6 5 3 3 2 1 2 4 7 5 3 3 5 4 5 2 4 3 5 3 7 5 7 3 7 2 4 7 5 4 3 3
##  [75] 2 4 7 5 4 2 6 4 1 1 2 3 5 4 5 2 6 5 2 4 5 4 5 5 2 4

Poisson Distribution

dpois(2,3)
## [1] 0.2240418
ppois(1,3)
## [1] 0.1991483
1-ppois(2,3)
## [1] 0.5768099
w=ppois(4,3)-ppois(2,3);w
## [1] 0.3920732
qpois(0.6,3)
## [1] 3
plot(1:4,ppois(1:4,3),type='s')