Problemas Impares Unidad II De Simulacion

1PROBLEMAS1.- Determine el ciclo o periodo de vida de los siguientes generadores congruencialesE)A)B)C)D)Xo=21Xo=21Xo=7Xo=23Xo=17X1=43a=21a=13a=17a=121a0=21c=15c=9m=31m=256a1=15m=31m=128m=64Xi+1=(aXi+c)mod(m)ri=Xi/(m-1)Xi+1=(aXi+c)mod(m)ri=Xi/(m-1)XrXrX220.73333333331000.7874015748190.63333333331380.541176470662120.4290.2283464567130.433333333330.011764705962190.633333333320.015748031540.13333333331240.4862745098110.3666666667350.275590551260.22450.9607843137290.9666666667800.629921259890.31100.43137254940.1333333333250.1968503937290.96666666672310.905882352960.2780.6141732283280.9333333333960.3764705882170.56666666671271110.36666666672170.8509803922001240.976377952810.0333333333820.3215686275150.5850.6692913386170.56666666672030.7960784314200.6666666667900.7086614173100.3333333333680.266666666710.0333333333270.2125984252150.51890.741176470650.16666666671040.818897637870.2333333333540.2117647059270.9810.6377952756260.86666666671750.6862745098240.8380.299212598480.2666666667400.1568627451230.76666666671190.937007874120.41610.63137254920.0666666667200.157480315180.6260.1019607843260.8666666667130.1023622047270.91470.576470588230.1500.3937007874250.8333333333120.0470588235160.5333333333190.1496062992220.73333333331330.5215686275100.33333333330020.06666666672540.996078431480.266666666790.070866141730.11190.4666666667280.93333333331260.9921259843200.66666666672400.9411764706140.46666666671110.8740157483011050.4117647059301440.3464566929140.46666666672260.8862745098250.8333333333690.5433070866210.7910.3568627451130.4333333333100.0787401575160.53333333332120.83137254990.3110.0866141732240.8770.3019607843180.6240.18897637850.16666666671980.7764705882210.7650.5118110236230.7666666667630.2470588235220.7333333333860.67716535431840.72156862751030.811023622490.1921568627680.53543307091700.66666666671250.9842519685350.137254902980.77165354331560.611764705930.0236220472210.0823529412480.37795275591420.55686274511210.952755905570.0274509804460.36220472441280.5019607843950.74803149612490.9764705882920.72440944881140.4470588235530.41732283462350.9215686275580.45669291341000.39215686271230.9685039372210.8666666667720.5669291339860.337254902490.38582677172070.811764705960.0472440945720.2823529412870.68503937011930.75686274511160.9133858268580.22745098041090.85826771651790.7019607843180.1417322835440.17254901961150.9055118111650.6470588235960.7559055118300.11764705881050.82677165351510.5921568627940.7401574803160.062745098790.62204724411370.537254902120.09448818920.0078431373370.29133858271230.48235294121060.83464566932440.95686274511070.8425196851090.42745098041200.94488188982300.9019607843330.2598425197950.3725490196540.42519685042160.8470588235710.5590551181810.3176470588360.28346456692020.7921568627930.7322834646670.262745098660.51968503941880.737254902990.7795275591530.2078431373160.1259842521740.6823529412890.7007874016390.1529411765140.11023622051600.6274509804630.4960629921250.0980392157600.47244094491460.5725490196210.1653543307110.0431372549260.20472440941320.5176470588910.71653543312530.9921568627400.31496062991180.462745098170.13385826772390.9372549021020.80314960631040.4078431373550.43307086612250.8823529412840.6614173228900.3529411765770.60629921262110.82745098041140.8976377953760.2980392157830.65354330711970.7725490196640.5039370079620.2431372549730.57480314961830.7176470588620.4881889764480.1882352941470.37007874021690.6627450981080.8503937008340.133333333350.03937007871550.6078431373740.5826771654200.0784313725750.59055118111410.5529411765880.692913385860.023529411810.00787401571270.4980392157220.17322834652480.9725490196390.30708661421130.443137254940.0314960632340.9176470588610.4803149606990.3882352941340.26771653542200.862745098670.5275590551850.33333333331120.88188976382060.8078431373570.4488188976710.27843137251100.86614173231920.7529411765310.2440944882570.2235294118280.22047244091780.69803921571170.9212598425430.1686274511220.96062992131640.6431372549590.4645669291290.113725490280.0629921261500.58823529411130.8897637795150.0588235294700.55118110241360.5333333333230.181102362210.0039215686520.40944881891220.4784313725450.35433070872430.9529411765820.64566929131080.4235294118510.40157480312290.8980392157320.2519685039940.368627451410.32283464572150.8431372549300.2362204724800.3137254902150.11811023622010.7882352941760.5984251969660.25882352941010.79527559061870.7333333333420.3307086614520.2039215686430.33858267721730.6784313725560.4409448819380.1490196078970.76377952761590.62352941181180.9291338583240.094117647170.05511811021450.568627451100.03921568631310.51372549022520.98823529411170.45882352942380.93333333331030.40392156862240.8784313725890.34901960782100.8235294118750.29411764711960.768627451610.23921568631820.7137254902470.18431372551680.6588235294330.12941176471540.6039215686190.07450980391400.549019607850.01960784311260.49411764712470.9686274511120.43921568632330.9137254902980.38431372552190.8588235294840.32941176472050.8039215686700.27450980391910.7490196078560.21960784311770.6941176471420.16470588241630.6392156863280.10980392161490.5843137255140.05490196081350.5294117647001210.47450980392420.94901960781070.41960784312280.8941176471930.36470588242140.8392156863790.30980392162000.7843137255650.25490196081860.7294117647510.21720.6745098039370.14509803921580.6196078431230.09019607841440.564705882490.03529411761300.50980392162510.98431372551160.45490196082370.92941176471020.42230.8745098039880.34509803922090.8196078431740.29019607841950.7647058824600.23529411761810.7098039216460.18039215691670.6549019608320.12549019611530.6180.07058823531390.545098039240.01568627451250.49019607842460.96470588241110.43529411762320.9098039216970.38039215692180.8549019608830.32549019612040.8690.27058823531900.7450980392550.21568627451760.6901960784410.16078431371620.6352941176270.10588235291480.5803921569130.05098039221340.525490196125511200.47058823532410.94509803921060.41568627452270.8901960784920.36078431372130.8352941176780.30588235291990.7803921569640.25098039221850.7254901961500.19607843141710.6705882353360.14117647061570.6156862745220.08627450981430.560784313780.0313725491290.50588235292500.98039215691150.45098039222360.92549019611010.39607843142220.8705882353870.34117647062080.8156862745730.28627450981940.7607843137590.2313725491800.7058823529450.17647058821660.6509803922310.12156862751520.5960784314170.0666666667

22.-

Datos1210.6875a=121113.53321210.6875c=55359.84941210.6875m=1771210.6875Xo=231210.6875media=0.691210.6875varianza=0.001210.6875Li v=0.111210.6875Ls v=0.061210.68751210.6875IntervaloOiEi=n/m(Ei-Oi)2/Ei1210.6875(0.00-0.10)691.001210.6875(0.10-0.20)1291.001210.6875(0.20-0.30)890.111210.6875(0.30-0.40)790.441210.6875(0.40-0.50)1090.111210.6875(0.50-0.60)1090.111210.6875(0.60-0.70)890.111210.6875(0.70-0.80)790.441210.6875(0.80-0.90)1090.111210.6875(0.90-1.00)990.001210.687587903.441210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.68751210.6875

33.-intervaloOiEi=n/m(Ei-Oi)/EiyXryxr[0,00-0,10)750.83289022589020.89021191630491630.9163[0,10-0,20)750.87924560424560.24568396056996020.9602[0,20-0,30)953.260319363190.03199219840419840.1984[0,30-0,40)5501017611760.0176393625693620.9362[0,40-0,50)350.83097630960.30968764704464700.647[0,50-0,60)750.8958521658520.58524186090086090.8609[0,60-0,70)350.83424590424590.2459[0,70-0,80)251.860466814660.0466[0,80-0,90)350.821715617150.1715[0,90-1,00)550294122594120.94129.88858574458570.5857x=62.0313430444930440.3044926593626590.2659la chi cuadrada de calculada es menor que la de tablas por lo tanto se acepta70702817020.070249280492800.9288611840011840.1184140185640180.40181614432414430.144320822498220.082267568475680.75685727462427460.2746754051654050.54052921402521400.214457960057960.57963359361659360.59363523609623600.236556960056960.56963244441644440.44441974913674910.74915611508111500.115132250032250.32251040062540060.4006160480364800.04823040030400.304924160024160.2416583705683700.837700569005690.056932376123760.2376564537664530.64534164120964120.64124111374411370.1137129276929270.2927856732956730.56733218292918290.1829334524134520.3452

44.-

0.87970.38840.38840.62890.87500.59990.85890.99960.24150.38080.96060.98480.34690.34690.79770.58440.81470.64310.73870.56130.03180.74010.45570.15920.15920.85360.88460.34100.14920.86810.52910.31880.59920.91700.22040.22040.59910.54610.57390.32540.08560.22580.46030.50270.83760.62350.62350.36810.20880.15250.20060.47200.42720.63600.0954

DatosIntervaloOiEi=n/m(Ei-Oi)2/Eimedia=0.5270.2122(0.00-0.10)450.20LI=0.4231.5646(0.10-0.20)350.80LS=0.58(0.20-0.30)450.20varianza=0.07(0.30-0.40)750.80Li v=0.12(0.40-0.50)450.20Ls v=0.05(0.50-0.60)953.20(0.60-0.70)450.20(0.70-0.80)350.80(0.80-0.90)851.80(0.90-1.00)450.2050508.40

55.-a=71Xo=167m=357A) PRUEBA DE CORRIDAS ARRIBA Y ABAJOXr760.2134831461s={0,1,1,0,0,1,0,1,0,0,1,1,0,1,1}410.1151685393550.154494382Co=103350.941011236=5%2230.62640449441250.351123595510.33333070.8623595506200.05617977532.52223490.98033707871460.4101123596-0.1321465387130.03651685392090.5870786517Z5%/2=1.962020.5674157303620.17415730341180.3314606742no se rechaza que lo nmeros del conjunto 1670.4691011236ri son independientesB) PRUEBAS DE CORRIDAS ARRIBA Y DEBAJO DE LA MEDIA S= { 0,0,0,1,1,0,1,0,1,0,0,1,1,0,0,0}Co= 9n0=10n1=62.93.251.8769230769como 1,87692308 cae dentro del intervalo 1,96 no se puede rechazar que los numeros del conjunto ri son independientes

66.- 0.140.380.120.40.740.780.430.670.620.320.530.540.240.820.940.190.980.4110.740.830.880.180.210.50.130.430.220.50.160.110.180.890.80.830.790.650.280.780.490.360.510.070.180.940.50.220.66

0.980.270.60.290.180.080.920.140.430.690.080.120.420.290.870.860.870.640.910.480.24

IntervaloOiEi=n/m(Ei-Oi)2/Ei(0.00-0.10)5102.50(0.10-0.20)15102.50(0.20-0.30)13100.90(0.30-0.40)5102.50(0.40-0.50)11100.10(0.50-0.60)11100.10(0.60-0.70)9100.10(0.70-0.80)11100.10(0.80-0.90)10100.00(0.90-1.00)10100.001001008.80

77.-TDTD1P1P1P2PTD1PTDTDTD1PTTDTDTD2PTDTD1P1PTTDTD1P1PTD1PTD2PTTDTTTD1PTDTDTDTD1PTDTDTDTDTD1PTD1P1PT1P1PTDTD1PTD1PTDT1PTD1PTDTDTD1P1P1PT1P1PTD1PTD1P1P1P1P1PTD1P1P2P1P1PTD1PTD1PTDTD1PTD1PTDTDTDTD2P1P1PTDTDTDTD1P2PTDTDCATEGORIAOiEi(Ei-Oi)/EiTD5255.440.21344877341P4447.520.26074074072P62.973.0912121212T83.964.1216161616P00.110.117.79701779711.833612.3904X=11.079.180916.3216el estadistico 7,797017797 es menor que x = 11,07 por lo tanto0.0121 se acepta que los numeros del conjunto ri son independientes

88.-0.780.980.240.730.430.160.780.040.290.680.770.160.030.790.960.260.910.550.750.550.640.610.140.380.120.40.740.780.430.670.620.320.530.540.240.820.940.190.980.4110.740.830.880.180.210.50.130.430.220.50.160.110.180.890.80.830.790.650.280.780.490.360.510.070.180.940.50.220.66

0.470.180.550.220.370.80.390.530.450.980.270.60.290.180.080.920.140.430.690.080.120.420.290.870.860.870.640.910.480.24

xyIntervaloOiEix20.780.04153.960.27313131310.040.96233.960.23272727270.960.61363.961.05090909090.610.43443.960.00040404040.430.82523.960.97010101010.820.83653.960.27313131310.830.22723.960.97010101010.220.83833.960.23272727270.830.51943.960.00040404040.510.981043.960.00040404040.980.291123.960.97010101010.290.261223.960.97010101010.260.141343.960.00040404040.140.671483.964.12161616160.670.941553.960.27313131310.940.881653.960.27313131310.880.51753.960.27313131310.50.791853.960.27313131310.790.071943.960.00040404040.070.242033.960.23272727270.240.682133.960.23272727270.680.912263.961.05090909090.910.382343.960.00040404040.380.622423.960.97010101010.620.192533.960.23272727270.190.18999913.880.180.160.160.65x2 de tablas= 33.1960.650.18como la calculada es menor Ho se acepta0.180.73 por lo cual los numeros son independientes0.730.770.770.550.550.120.120.320.320.980.980.210.210.110.110.280.280.940.940.430.430.160.160.750.750.40.40.530.530.410.410.50.50.180.180.780.780.50.50.160.160.030.030.550.550.740.740.540.54110.130.130.890.890.490.490.220.220.780.780.790.790.640.640.780.780.240.240.740.740.430.430.80.80.360.360.660.660.470.470.220.220.390.390.980.980.290.290.920.920.690.690.420.420.860.860.910.910.180.180.370.370.530.530.270.270.180.180.140.140.080.080.290.290.870.870.480.480.550.550.80.80.450.450.60.60.080.080.430.430.120.120.870.870.640.640.24

99.-1280860889262834616018367690334104660884149741016540909635691215649935556913408913191170468642977515media42650.74463024836042288459821227630398850615023016918489069316536933711843056929389115003043051163813057414052476174401127416008536232772255864475134892854051prueba de corridas arriba y abajoS={ 1,0,1,0,1,0,1,0,0,1,1,0,1,1,0,0,1,1,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0,1,1,0,1,0,1,1}Co=31=5%338.5666-0.2334Z5%/2=1.96el estadistico Zo es menor que el de la tabla por lo tanto no se rechaza que los numeros del conjunto son independientes B) PRUEBAS DE CORRIDAS ARRIBA Y DEBAJO DE LA MEDIA S={0,1,0,1,0,1,0,1,0,0,0,1,0,1,1,0,0,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,1,0,1,1,1,1}Co= 28n0= 24n1= 2625.4612.20490.208113como 0,208113 cae dentro del intervalo 1,96 no se puede rechazar que los numeros del conjunto ri son independientesPRUEBA DE POKER12808608892628346160183676903341046608841497410165409096356912156499355569134089131911704686429775154630248360422884598212276303988506150230169184890693165369337118430569293891150030430511638130574140524761744011274160085362327722558644751348928540511P1P1P1PTD1P1P1PTD1P2P1P1P1P1PTDTTDTD2PTDTD2PTD1P1PTD1P1PTDTDT1PTD1P2P2P1PTD1PTD1P1P1P1PTP1PTD1P1PCATEGORIAOiEi(Ei-Oi)/EiTD1515.120.0009523811P2725.20.12857142862P55.40.0296296296TP10.450.6722222222T23.60.7111111111P00.2250.225Q00.0050.0051.77248677250.0144X=12.5923.240.160.30252.560.0506250.000025el estadistico 1,77248677 es menor que x = 12,592 por lo tanto se acepta que los numeros del conjunto ri son independientes

1010.-ho= independientesh1= dependientes0.60690.53160.05290.91310.29910.68480.82910.49110.81950.35210.80680.10620.60840.92870.040690.25490.10030.55230.18970.87250.44390.19260.02660.56960.75040.85420.60450.22690.63670.95430.53850.25740.23960.34680.41050.12330.29970.94810.79540.72710.57390.60560.8310.17090.7970.37380.12840.51430.20140.99S=(0,0,0,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,1,0,0,0,1,1,1,0,1)Co = 26338.5662.3917como el estadistico Zo es mayor al valor critico de Z/2 , por lo tanto se concluye que los numeros del conjunto rj no son independientes.

1111.-S={ 1,1,0,0,0,1,1,0,0,1,0,1,0,0,1,1,0,1,0,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,1,1,1,0,1,0,1,0,1,0}Co=28no=24n1=2625.4612.20490.208113como 0,208113 cae dentro del intervalo 1,645 no se puede rechazar que los numeros del conjunto ri son independientes

1212.-Nivel de aceptacion90%xy0.58580.8863intervalo iOiEi = (n-1)/m; 49/25 Xo= (Ei-Oi)^2/Ei0.88630.83780.83780.3203111.960.47020.32030.4115221.960.00080.41150.2710311.960.47020.27100.9238401.961.96000.92380.1959541.962.12330.19590.9268621.960.00080.92680.6702701.961.96000.67020.6213831.960.55180.62130.4360901.961.96000.43600.62791021.960.00080.62790.84151111.960.47020.84150.57861221.960.00080.57860.05431311.960.47020.05430.35671421.960.00080.35670.16551521.960.00080.16550.33801601.961.96000.33800.80801701.961.96000.80800.19311831.960.55180.19310.08431921.960.00080.08430.91522041.962.12330.91520.60932131.960.55180.60930.75872221.960.00080.75870.45152331.960.55180.45150.32032441.962.12330.32030.51392551.964.71510.51390.7070Total494924.97960.70700.91230.91230.12420.12420.88260.88260.99210.99210.85230.85230.67230.67230.85400.85400.47220.47220.47810.47810.21010.21010.16800.40280.86580.86580.40280.40280.61360.61360.87200.87200.11260.11260.58570.58570.91720.91720.89430.89430.80950.80950.64081323.0000450.8003.0000240.6121.0000220.4203.0000020.21210400.20.40.81El valor de tablas X = 33.196 es mayor que el error total de 31.250, por lo cual podemos rechazar la hipotesis de independencia.

1313.-0.895663250.923521820.172909930.250569870.895663250.160429390.172909930.88053740.250569870.624025920.160429390.669772570.88053740.815206310.624025920.584687620.669772570.851605680.815206310.581193710.584687620.722740650.851605680.839092180.581193710.865315460.722740650.144002360.839092180.639979370.865315460.816711190.144002360.857141190.639979370.051854750.816711190.040511740.857141190.428714220.051854750.012889590.040511740.819892160.428714220.512130240.012889590.632189150.819892160.486052890.512130240.444643720.632189150.853876670.486052890.532732740.444643720.144890230.853876670.58906440.532732740.159124270.144890230.491450850.58906440.194063430.159124270.824815710.491450850.822841070.194063430.801717510.824815710.863290470.822841070.198350380.801717510.476508830.863290470.223978930.198350380.49704920.476508830.160600390.223978930.354758310.49704920.317797870.160600390.660417210.354758310.359393530.317797870.37764780.660417210.520395550.359393530.560669750.37764780.051206610.520395550.779964150.560669750.997551960.051206610.484017750.779964150.872488590.997551960.026657250.484017750.82569510.872488590.571967680.026657250.16422970.82569510.015173340.571967680.723213520.16422970.98114460.015173340.483713790.723213520.753190260.98114460.069303950.483713790.387295240.753190260.624092570.069303950.424645140.387295240.899030550.624092570.811735990.424645140.568809910.899030550.595494370.811735990.837369150.568809910.198771420.595494370.115385060.837369150.807739940.198771420.716481070.115385060.380695840.807739940.612681740.716481070.499330190.380695840.128548740.612681740.293007550.499330190.455473330.128548740.020095710.293007550.364572230.455473330.272664750.020095710.149036040.364572230.334907490.272664750.40113280.149036040.273842340.334907490.829350650.40113280.923521820.273842340.110906580.829350650.043842570.110906580.044039770.662241040.723028020.043842570.885305320.044039770.273263110.723028020.854492990.885305320.798267540.273263110.704398490.854492990.809819690.798267540.735217960.704398490.58058570.809819690.175225270.735217960.881854380.58058570.327280470.175225270.540664890.881854380.589307230.327280470.939281970.540664890.628689950.589307230.480092870.939281970.048607710.628689950.755347480.480092870.200589710.048607710.61226830.755347480.948523770.200589710.43436080.61226830.615338560.948523770.00060210.43436080.104633950.615338560.662363150.00060210.28447020.104633950.455924990.662363150.969367680.28447020.470298330.455924990.907952350.969367680.026834630.470298330.057968750.907952350.131935980.026834630.143633510.057968750.628685120.131935980.808709860.143633510.946178820.628685120.710909540.808709860.522969730.946178820.790317760.710909540.533012430.522969730.001493360.790317760.973173950.533012430.56310490.001493360.012272970.973173950.329246210.56310490.100734480.012272970.424117430.329246210.400230770.100734480.937953460.424117430.329891440.400230770.638599250.937953460.251493930.329891440.599676880.638599250.107775850.251493930.431919730.599676880.802311730.107775850.32936060.431919730.571629390.802311730.980325170.32936060.851020490.571629390.622101060.980325170.429370590.851020490.698542270.622101060.496507550.429370590.043847990.698542270.021074570.496507550.323127420.043847990.534434730.021074570.15815470.323127420.112868210.534434730.52144060.15815470.761487070.112868210.134598620.52144060.946979340.761487070.788150650.134598620.186209590.946979340.311292210.788150650.009467020.186209590.607691530.311292210.865088670.009467020.810861730.607691530.654072430.865088670.224460490.810861730.384581710.654072430.713606230.224460490.042120540.384581710.216597960.713606230.662241040.042120540.547478160.216597960.020804330.547478160.508121960.020804330.150068320.508121960.398071270.150068320.321997980.398071270.02274080.321997980.959290120.02274080.091356250.959290120.527487490.091356250.920850980.527487490.79326550.920850980.313251790.79326550.015454680.313251790.01545468

140.58580.88630.83780.32030.41150.2710.92380.19590.92680.67020.62130.4360.62790.84150.57860.05430.35670.16550.3380.8080.19310.08430.91520.60930.75870.45150.32030.51390.7070.91230.12420.88260.99210.85230.67230.8540.47220.47810.21010.1680.86580.40280.61360.8720.11260.58570.91720.89430.80950.6408media=0.57486var=0.0784No son los mismos que los de uan distribucion uniforme de numeros pseudoaleatorios, se atribuye la diferencia a la forma empirica en que fueron concevidos quizas

1515.-CATEGORIAOiEi(Ei-Oi)/EiTD13851140402.54423076921P546452657.5215574549T2151952.051282051312.11707027543572139601X=7.815400el estadistico 12,1170703 es mayor que x = 7,815 por lo tanto no se acepta que los numeros del conjunto ri son independientes

1616.-FOPEFEX2TD0.30241P0.5042P35000.10877222308.37661T0.0721F0.009P0.0045Q0.0001n71500EL ERROR DE ESTE EVENTO ES DE 2308.3766

1717.-si aceptaria la hipotesis de independencia

18

n=71500D=42 pares=3500

CategoriaProbOiEiError2P0.02735001930.51276.0063455064

1919.-n=3575002p17500

CATEGORIAPROBA.Oi E1 2p0.108175003861011541.8829318829

Se rechaza la hipotesis de independencia

20A) No necesariamente se puede hacer con numeros de 3,4 y 5 y quizas hasta mas pero utilizando solo 5 digistosb)Falso, pues para estar completamente seguros que son numeros aleatorios deben de pasar las 4 pruebas, media, varianza, uniformidad e independenciac) Cierto, esto quiere decir que los nuemros estan dispersos en todo el espacio disponible.d) Cierto, pues al tener una media de 0.5 y una varianza de 1/12 se dice que los numeros tienen una priobabilidad uniforme continua

2121.-928590938898939096918688100858481Ho= independienteH1= dependienteintervaloOiEi=n-1/m1100901.1111111111285900.2777777778384900.4481900.9596900.4691900.0111111111786900.1777777778888900.0444444444988900.04444444441098900.71111111111193900.112909001392900.04444444441485900.277777777815909001693900.1144014404.6x=24.996mi X de tablas es mayor que la calculada por lo tanto Ho se acepta

22n=17000alfa=5%alfa2=0%media=11333var=3021.9

Zo=|(Co-media)/var|Co=Zo*Var+media

Comin=11484Comax=11333

2323.-0.522205430.466890690.634299370.398935860.512107330.563049210.501217690.835473720.277798520.053672210.351410180.717342130.470609160.705970230.107700640.295619210.038494170.575990830.431334770.084885530.585411180.378604940.720018980.526318620.51352640.658784760.617539450.501315480.146484570.807766620.378729940.835755050.315404430.966741420.277847720.324544680.059101830.346359990.250424060.093924220.462233930.438613720.220953920.843553340.534827430.584500830.548437910.342062610.170020280.688805640.094126150.626721390.925168470.894297240.706429590.765187710.367666050.483315440.856983250.203733360.223648020.436470840.157616610.246329120.706634060.376010830.435276930.360225580.970661790.373308090.60119470.504917050.286502690.911823240.684193650.775787960.812829210.139576480.925996520.853156650.252785560.885245780.375478340.04960240.151124220.917279140.854713270.004970520.070565330.332930050.968574260.973094790.14298410.803072180.300801960.811545370.41314570.367627670.544018530.85997823prueba de mediasprueba de varianzaHo: ri=o.5Ho: ri=1/12H1: rio.5H1: ri1/12media=0.494689469varianza=0.0736261686LI=0.4434196736LI=0.1080963805LS=0.5565803264LS=0.0617550505Ho se aceptaHo se aceptaprueba de uniformidadHo= ri es uniformeH1= ri no es uniformeintervaloOiEi=n/m(Ei-Oi)/Ei[0,00-0,10)9100.1[0,10-0,20)7100.9[0,20-0,30)10100[0,30-0,40)16103.6[0,40-0,50)9100.1[0,50-0,60)14101.6[0,60-0,70)7100.9[0,70-0,80)7100.9[0,80-0,90)13100.9[0,90-1,00)8100.41001009.4x=123.2222la x calculada es menor que la de tablas por lo tanto se acepta Ho

24

Tamao del huecoFrecuencia Observada Ei=(h)(-)(-)i Ei=(40)(0.1)(1-0.1)(Ei-Oi)2/Ei054.000.25143.600.04233.240.02332.920.00>32526.240.06Total40400.37-=0.1a)0.37332.920.00>32526.240.06Total4029.160.06-=0.1a)0.06b)=10%X2,0.1,3=6.251R=La muestra es pseudoaleatoria ya que Xo2 es menor que X2n=17000alfa=5%alfa2=0%media=11333var=3021.9

Zo=|(Co-media)/var|Co=Zo*Var+media

Comin=11484Comax=11333

2525.-ho= independientesh1= dependientes5(0.5,0.8)S={ 1,0,0,0,0,0,0,0,0,1,1,0,1,0,1,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,1,0,0,0,1}0.58580.88630.83780.32030.41150.2710.92380.62130.4360.62790.84150.57860.05430.35670.19310.08430.91520.60930.75870.45150.32030.12420.88260.99210.85230.77230.8540.47220.86580.40280.61360.8720.11260.58570.91720.19790.92680.67020.16550.3380.8080.51390.7070.91230.47810.21010.1680.89430.80950.6408

H=12=0.5=0.8

Tamao del huecoOiEi= (h)(-)(1-(-))i

033.60.1122.520.1073015873221.7640.0315736961311.23480.0446477486400.864360.86436542.016841.950042435512X0=3.0979254676

X^2,m-1=11.07se acepta H:o