頻率的穩(wěn)定性——模擬投硬幣實(shí)驗(yàn)及其推廣

1、伯努利隨機(jī)數(shù)（0-1隨機(jī)數(shù)）（0-1）區(qū)間均勻分布隨機(jī)數(shù)實(shí)驗(yàn)次數(shù)2000.19815668210.962309641伯努利均勻分布00.133610034 正面次數(shù)101210.265205847 正面頻率0.50.600.32367931210.118045595 試驗(yàn)次數(shù)5000.336863308伯努利均勻分布10.840998566 正面次數(shù)262000.447920164 正面頻率0.520.410.96612445410.804376354 試驗(yàn)次數(shù)10010.382030702伯努利均勻分布00.058717612 正面次數(shù)455610.238593707 正面頻率0.450.5

2、610.252265999 試驗(yàn)次數(shù)100000.502059999伯努利均勻分布10.528305918 正面次數(shù)50949100.678792688 正面頻率0.5090.49100.37116611200.867976928 試驗(yàn)次數(shù)2000伯努利均勻分布伯努利隨機(jī)數(shù)（0-1隨機(jī)數(shù)）（0-1）區(qū)間均勻分布隨機(jī)數(shù)正面次數(shù)100999110.113162633 正面頻率0.50450.495500.90279854700.68370616800.71541489910.52586443700.79149754310.16293832210.26563310600.63969847710.97

3、073274910.61955626100.24304940900.67580187400.92815942910.63795892210.25199133300.24726096400.04556413510.90917691600.21033356700.12845240610.91656239510.40308847300.45692312410.05722220500.56419568510.83989989910.96261482600.22690511800.59077730610.36631366910.92617572600.6236762600.7901242100.8435

4、621200.53611865600.86611529910.25421918410.6524246961070287179210.50514236910.42252876410.88091677600.82488479300.68364513110.59147923210.247138891032563249600.47184667500.36677144710.85363322910.97531052610.07202368200.27103488300.08282723500.29154332100.62144840800.599230

5、93410.75713370210.52873317710.42078920910.79522080110.00598162810.41392254400.44181646200.98544267100.82592242200.3314920500.91082491500.8527787100.58259834600.44044312900.08172856810.94250312810.2188787500.67647328100.35496078410.93090609510.57359538600.42008728310.39802240110.88811914410.718131046

6、00.11197241100.42457350410.06625568400.71672719510.59681997110.28772850710.24445326100.71712393610.47700430300.54411450510.16138187800.77715384400.2572099980006723227610.3341471600.56135746310.91061128600.92602313310.72322763800.20307016200.44343394300.29935605910.65044099210.3908200321

7、0.63811151510.44352549800.02740562200.84914700810.44254890600.6500747700.073519089100274361400.362407310.09195226900.94576860910.02041688310.0986968600.82561723710.6537675110.96060060400.71263771500.79967650400.92641987400.63032929500.02359080800.55659657610.63499862700.42011780100.3469

8、954530088055055400.3828852200.95620593910.08261360500.402081362100075685900.25861384910.1510971400.25312051810.95962401200.24921414810.31296731500.8259529400.16663106210.11001922700.00976592310.74150822500.89172032810.99035615110.79039887710.3716238900.37656788810.537064731

9、0.76543473600.74340037200.94280831300.07699819900.58000427300.545121616105287331770055616931700.65550706500.52073732700.39771721500.96157719700.3474532310.47273171210.20252082900.33240760500.5761589400.67085787510.23068941310.55403302110.4715414910.8685567800.29285561700.48

10、207037600.10373241410.44370860910.99005096600.60881374600.60972930100.64409314210.10296945110.52021851300.94689779400.95159764400.62401196300.42545854100.42970061300.09701834200.83767204810.5397198410.70601519810.75658436800.35648670910.60200811800.32880642100.4611041600.51817377210.30878627910.5802

11、4842110.74953459300.05011139310.94509720100.70354319900.09772026710.4080629900.99383526110.19953001510.65395062100.69457075700.0051271100.3439741200.31220435200.56401257400.5067598500.5816217541001989806810.2364879300.95358134710.79528183810.51149021900.47813348800.21411786210.652699362

12、00.2348399300.78258613800.79335917210.68938261100.04574724600.85439619100.26148258900.64235358710.89001129200.88610492300.45170445910.2802209541012067018600.89715262310.71694082510.86620685400.92413098500.73882259600.31311990700.0832850120076039918210.19675283100.4876857811

13、0.06823938700.70616779100.93429364910.4821924500.66856898700.53852961800.38312936810.76058229300.56990264610.79113132110.25739310910.73577074500.36783959510.67390972610.43745231510.73595385610.67024750510.08645893700.55500961310.37415692610.61296426300.19583727510.88494521910.99826044500/p>

14、.73488570800.07477034800.62691122200.79741813410.67775505800.74361400210.27851191700.41712698800.44846949700.48106326500.09860530400.31431012900.31913205410.27823725110.1926633510.4368724630092129276410.5698721270015265358410.3791924810.10477004310.99700918610.7594225910.71

15、718497300.9228186900.1271401100.37611011110.5663319810.11545152110.81536301810.05407879910.68144779810.19217505410.71138645600.80950346410.617908261101857051300.7227698600.0589617600.74092837300.52507095600.47703482200.82461012610.32142094200.26267281100.4928434100.09332560200.560991241

16、10.42435987410.31421857410.86825159500.04461806110.97210608210.40339365810.21817682400.69911801510.22592852600.9997863700.32584612600.77367473410.54594561600.19959105200.87359233410.80770287210.05475020600.912778110.79842524500.49055452110.68279061300.85247352510.94750816400.82049012710.31669057310.

17、21466719600.6650288400.46842860210.33268227210.20310068100.84224982500.75331888810.29602954210.05624561310.4614703820010742515310.73250526410.16568498810.63005462810.3783684800.90978728600.88442640500.06009094510.31580553600.45588549510.0479140600.53321939800.89815973410.02584917810.420

18、1483200.0704367200.62349314910.94238105410.08246101300.7799005110.61125522610.01565599510.59859004500.48637348610.33854182610.45933408610.89278847610.22229682310.79280983910.55778679800.8720358900.48597674510.32132938610.24213385400.32358775600.67390972600.95968504900.23044526510.11926633510.5931272

19、3210.51966917910.8886074410.25742362700.45985290100.21829889810.46836756500.77437665900.29078035810.12915433210.87841425810.05587939110.09302041710.23715933700.64488662410.58058412410.75939207100.37818536910.21774956510.62608722210.07464827400.8445997510.27896969510.96929837900.73992126200.938169500

20、.20889919700.11209448510.82015442400.25135044410.36729026200.06381420300.52238532700.95861690110.34464552800.21134067810.70992156700.89831232600.8411206410.30857264910.05905331610.72734763600.32786034710.11603137310.26505325500.9290444650072261726700.20264290300.95574816110.21597949210.

21、07947019900.44828638610.28760643310.9613025310.7788628800.06970427600.68868068510.69069490610.60759300500.08954130700.44114505410.00701925710.90780358300.52885525110.83986938100.45225379200.275185410.436933510.72743919210.02615436310.62651448110.81402020310.35190893300.73918881810.16751609900.832361

22、82700.32773827300.85393841410.29248939510.26279488500.98159733910.9727774910.94665364510.51240577400.86428418810.62743003610.4826502271070983001210.52653584400.54274117310.53413495310.62303537110.1177404110.9971312610.82461012610.77697073310.62077700110.47062593500.82573931110.401287881

23、1048820459600.52555925210.34296700910.3421430110.7710806600.36249885610.98040711700.36976226110.71431623300.91756950600.77242347510.78820154400.57734916200.46742149100.22327341510.58134708700.41880550610.30561235410.54481643110.33683278900.30646687210.237098310.7972960600.94869838600.83

24、4009827107897274710.04089480300.4756309700.09241004700.52165288200.7678151800.80993072300.69493697900.4467909790014377269800.45442060610.34034241810.58592486300.5683767210.67595446600.05108798510.74355296500.97778252510.54506057910.91955320900.4082766200.0816980500.21414838

25、10052320932600.94393749810.31296731500.8703878900.03033539810.07684560700.78899502510.30411694700.68459120500.62450025900.4842371910.59660634210.49482711310.66417432210.35465559910.81603442510.94814905210.1588793600.73821222610.76723532810.67354350410.59123508410.57829523600.94680623800

26、.70137638510.8102053910.00823999810.41422772900.97463911900.12198248200.20346690310.86049989310.2685323650090752891600.6550492871054045228410.5381939151030500198410.9076509910.27979369500.04040650710.37495040700.27967162100.06836146110.00946073800.31684316500.3

27、4595782300.87527085200.52693258510.08499404910.67574083710.19611194200.99493392700.30545976110.3932309951007477034810.42811365110.34650715700.10287789500.4588457910.53688161900.3020111710.19772942300.87029633510.474196610.19565416410.73784600400.57325968210.4365367610.97186193400.788933

28、988106965544610.04150517310.93115024300.99227881710.60866115310.89077425510.55821405700.7915585800.55397198400.8709982610.6321909241098089541300.70180364400.2992339851019772942310.7184667510.27298806700.10635700610.07361064500.39420758710.39185766200.1413617360

29、0.30365916900.16971343110.25632496100.21127964100.39487899400.12002929800.35267189600.22312082310.02920621410.49089022510.5691091650095953245610.63539536700.51091036700.63948484800.09530930500.38221381310.52055421600.72124393410.93392742710.36695455800.80919827900.89452803100.9936521510

30、.35715811610.60567033900.37757499910.4054078810.10330515500.72942289510.9997863700.31846064610.74608600110.49336222400.11758781710.27698599210.31147190810.34333323210.32190923810.22373119310.3253273110021735282410.2866603600.07806634700.48847926300.05529953910.00518814710.57109286810.02

31、645954810.5014801480067604602210.06894131300.31977294210.8073366500.5382854700.52400280800.25318155500.8400830100.75576036910.48112430210.88323618310.45530564300.36439100310.37983336900.74941251910.96102786300.16159550810.16446424810.50929288610.41224402600.39860225200.33182775410.42109

32、439400.28861354410.37339396300.27732169610.92992950200.86104922600.95541245810.84652241610.63826410710.40427869500.5726798310.49769585300.44315927610.91146580400.6936857210.98232978310.12009033500.46668904710.3341471600.94903408910.1357463300.93224890900.62068544610.37788018410.9703054910.1063264871

33、0.94222846200.25092318500.73082674610.00799584900.72069460100.36530655810.337015910.44505142400.33213293910.69508957210.0603961300.52140873410.20917386400.2084414200.6982024600.24045533600.65672780510.54588457910.16330454410.86004211600.411542110.46623126900.7715994750047749259900.46635

34、334310.0075685900.24854274100.26706747600.48094119100.0499893191058122501300.06875820200.83831293710.70567949510.45789971600.9913937800.96145512300.01696829110.42133854210.5905941950012622455510.1627857300.87130344600.65419476910.9919736321069521164610.28516495

35、300.48823511500.43620105600.99261452100.40708639800.55864131600.48088015400.39759514110.6552323981021204260400.21362956610.66460158110.32499160700.66289254410.1152684100.58983123310.48103274610.93270668710.49250770610.69698171900.04663228200.76427503310.84401989810.80886257500.096682638

36、00.8028199100.12530910.88543351500.77135532710.06765953600.45857112310.51994384600.91250343300.66832483900.10946989310.63234351600.10840174600.2957548750014136173610.80254524410.52031006800.63191625710.89632862300.62340159300.42768639200.91906491300.64970854810.59117404700.62385937100.6

37、8248542700.35239722910.357554857103667104100.55226294710.1351359600.27204199300.792138432104723654910.87554551810.38016907300.48500015310.53056428700.16476943300.89623706810.45927304900.01910458700.52980132510.11612292910.43507187110.44499038700.41279335900.3228858300.23368

38、022700.8333384200.77236243810.03985717300.58842738110.57438886710.16638691410.9061861021055439924310.98583941210.10126041410.80257576210.22519608110.86959440900.224402610.72139652700.77013458710.8327280500.03546250810.70412305110.0213629570096346934400.3061006500.2860805080

39、0.44688253410.78865932210.411542110.73641163400.26667073600.40501113900.57152012700.52046266100.24982451900.06881923910.88286996110.25031281510.35157322900.03988769210.68971831400.02319406700.39225440200.02163762300.88811914410.63182470210.05069124400.30628376100.11563463200.12085329800.82033753500.

40、03115939800.60713522810.34513382410.95953245600.45301675500.99731437110.68602557510.96725363900.64564958610.85232093310.58226264200.61546678100.52793969510.21076082610.03170873110.06939909110.62822351800.9160435800.71977904600.12686544410.49107333600.02044740100.93118076100.108096561100

41、4348887610.90112002900.42701498510.45295571800.36423841110.76219977400.3757133710.00515762800.53028962110.7433088170003796502610.76360362610.77669606610.66722617300.20777001310.44508194210.1693166911087255470410.85882137500.4952848910.09649952710.3716238910.97729422910.3648

42、1826200.59611804600.1984008310.56901760900.22681356210.5378887310.47148045300.40961943400.86043885610.76635029100.61104159700.8775597400.71285134400.69249549910.62669759200.71599475110.73857844810.40046388100.92272713410.24192022500.89724417900.77953428810.02713095510.78386791610.9656056400.71263771

43、51062907803600.82058168310.85290078400.98388622710.26209295900.84884182300.01922666100.631916257106398510700.74245429900.10492263600.03360087910.61848811310.99276711310.25824762700.47224341610.77294228900.62047181610.59614856410.3129367960054063539510.842799158

44、00.47553941500.16800439510.19306009100.6869411300.36890774300.72038941610.30915250110.60673848700.04138309900.69826349710.5165257731087240211210.1163060410.81255531510.79280983910.08606219710.68129520610.4387646111086883144600.5651417580040363780600.37119663100

45、.52372814110.66579180300.64525284600.37601855510.01751762400.56767479510.06506546200.91384624810.49064607710.45298623610.80166020700.60670796810.46418652900.09686574910.01437421810.02175969700.60029908100.92162846800.71031830810.8161259810.39313943910.54853968910.21350749210.9535203110.64336069810.0

46、0015259310.68333994600.77489547410.37153233400.58433790110.58751182600.20355845800.32776879210.99081392910.53694265610.86648152110.7528611110.63228247900.38767662610.41261024800.54802087500.76076540400.01709036510.8099917600.50877407110.39042329200.67986083600.90249336200.77980895400.55870235300.350

47、38300710.0076296270095596179110.9578234210.83657338210.59953611900.4561906800.91979735700.51765495810.99008148400.57890560610.88140507210.00476088700.3288369400.41410565510.06537064710.6517227700.98861659600.0412915430023374126410.80419324300.9739982310.01019318210.19772942

48、310.44715720100.66081728610.44032105500.77089754910.74825281500.26816614300.3695791500.53068636110.80510879800.74730674210.0086062200.30808435300.6177556691010119937710.60747093100.49803155610.68376720510.79815057810.20932645610.90557573210.9487594230079946287410.685903510.

49、23899044800.54536576400.4201483210.84142582510.65904721200.80697042800.52510147400.49204992800.906308176109189428391097705008100.29517502400.3627430041086700033600.19516586810.12707907310.9780877100.79680776410.78945280300.27317117810.51277199600.99453718700.62

50、877285100.94418164610.47392193410.56575212910.42017883800.447218238104831385241040797143500.12189092710.226050610.45847956800.77849665800.31110568600.10202337710.46284371500.97988830200.72954496900.78106021310.61705374310.96105838200.40195928810.07403790410.33259071600.4547

51、563100.72838526610.48664815200.475844600.21198156710.90548417600.57969908700.41157261910.4963225210.5688039800.66765343210.03292947210.61912900210.31205175910.88607440400.68379772300.79720450510.2392956330038026062810.11371196610.20694601310.10061952600.23685415210.86413159610.911130100

52、.37379070400.50440992510.06796472110.4772789700.55030976310.12524796310.42805261400.70778527210.99114963200.21237830700.51789910600.64412366110.78524124900.3587145600.4793237100.59962767400.2761619920001074251510.31943723910.20770897510.01544236600.92788476200.42332224510.01974547600.13

53、989684700.07788323610.78820154410.32615131100.48048341310.88836329210.02633747410.10507522810.1576586210.33225501300.71538438100.63393047910.80874050110.59019745500.53666798900.69917905210.08233893910.19113742510.97799615510.11331522610.21356852900.91299172910.75710318310.06927701710.08487197500.223

54、88378600.62205877910.36439100300.6799829100.54637287500.68492690800.02426221500.33631397410.12436292600.94479201610.35889767110.70274971810.7754448071098107852400.8085573910.3087557610.7014679400.81929990500.149876410.89068269900.61659596500.65599536100.20023194110437574389

55、10.22238837900.25083162900.22327341510.01306192200.3812372210.98748741110.76662495810.9457380910.42860194710.70979949310.80526139100.81640064710.04620502300.59959715600.61278115210.84783471210.93551438900.94396801700.65453047310.16412854410.66408276610.71996215700.45872371600.3020111700.75704214600.

56、44679097910.68517105600.1304361100.56297494400.7117831970083468123410.92721335510.27637562210.24250007610.12076174210.20245979210.16876735700.05316324400.29755546710.62907803610.66866054310.26334421810.39118625410.61513107710.59114352900.80901516810.94973601510.94872890400.77565843700.0

57、61006510.69301431310.4727317120014957121510.66469313600.25400555410.52882473210.73564867110.04235969100.77776421410.79400006110.01123081110.2622760710.1986144610.62739951800.20920438210.6146427810093865779600.4041871410.96584978810.35084078500.6515091400.88579973810.7640614

58、0310.91680654300.00354014700.88515884900.98416089400.44764549700.300576810.93661305600.16821802410.38187810900.53245643510.6549882510.21845149110.27338480810.75658436800.21033356700.0976592300.31427961110.65511032410.28135013910.09466841610.1638843961076815088400.81029694500.61601611410

59、.63811151510.04644917100.5201574760028458510100.0438245800.07095553510.79326761710.56074709310.91961424600.96594134310.6376232181062913907310.7960753210.02258369710.1156346320067357402310.93456831610.02185125310.68370616810.82302316400.84273812110.53465376800.5

60、1377910710.98739585600.10644856100.31067842610.97033600910.80471205810.47053437910.63951536600.11297952210.81139561100.67961668800.72539445210.51518295810.22916348810.74279000200.0178228100.89693899300.1912289810.8802148510.49760429700.89281899510.56407361110.68230231610.32364879310.73540452310.0213