BernoulliDistribucin BernoulliXf(X)F(X)XF(X)00.7000000.700000-100.0000000.00000010.3000001.000000010.7000000.700000121.0000001.000000

Bernoulli

XF(x)Funcin de distribucin de Probabilidad Bernoulli p=0.3

Binomial

Xf(X)Funcin de probabilidad Bernoullip=0.3

PoissonDistribucin BinomialXf(X)F(X)XF(X)00.1176490.117649-100.0000000.00000010.3025260.420175010.1176490.11764920.3241350.744310120.4201750.42017530.1852200.929530230.7443100.74431040.0595350.989065340.9295300.92953050.0102060.999271450.9890650.98906560.0007291.000000560.9992710.999271671.0000001.000000

Poisson

f(X)Xf(X)Funcin de probabilidadBinomial n=6, p=0.3

Uniforme

XF(x)Funcin de distribucinBinomial n=6, p=0.31.000

GammaDistribucin Poisson0.25Xf(X)F(X)XF(X)00.778800.77880-100.000000.0000010.194700.97350010.778800.7788020.024340.99784120.973500.9735030.002030.99987230.997840.9978440.000130.99999340.999870.9998750.000011.00000450.999990.99999561.000001.00000

Gamma

f(X)Xf(X)Funcin de probabilidadPoisson =0.25

Beta

XF(x)Funcin de distribucinPoisson =0.25

NormalDistribucin Uniformeenen otro caso =8 =31 / ( - )0.2Xf(X)2300380.20.28900enenenXF(X)2.502.602.702.802.90303.10.023.20.043.30.063.40.083.50.13.60.123.70.143.80.163.90.1840.24.10.224.20.244.30.264.40.284.50.34.60.324.70.344.80.364.90.3850.45.10.425.20.445.30.465.40.485.50.55.60.525.70.545.80.565.90.5860.66.10.626.20.646.30.666.40.686.50.76.60.726.70.746.80.766.90.7870.87.10.827.20.847.30.867.40.887.50.97.60.927.70.947.80.967.90.98818.118.218.318.418.51

Normal

Xf(X)Funcin de densidad Uniforme =3 y =8

Log-Normal

XF(X)Funcin de Distribucin Uniforme =3 y =8

IC MediaDistribucin Gamma=1 y =1=2 y =1=4 y =1=1 y =1=1 y =2=1 y =4=1 y =1=2 y =1=4 y =1=1 y =1=1 y =2=1 y =4Xf(X)f(X)f(X)f(X)f(X)f(X)F(X)F(X)F(X)F(X)F(X)F(X)00.00000000000000000000000.0000000.0000000.0000000.0000000.0000000.0000000000000000.0000000.0000000.0000000.0000000.0000000.10.09516258192629430000000.0046790.0000040.0951630.0487710.0246900.0951625819498300.0046790.0000040.0951630.0487710.0246900.20.0861070.0128440.0000530.0861070.0463920.0240800.1812690.0175230.0000570.1812690.0951630.0487710.30.0779130.0194130.0002090.0779130.0441290.0234860.2591820.0369360.0002660.2591820.1392920.0722570.40.0704980.0246160.0005100.0704980.0419770.0229060.3296800.0615520.0007760.3296800.1812690.0951630.50.0637890.0286520.0009750.0637890.0399300.0223410.3934690.0902040.0017520.3934690.2211990.1175030.60.0577190.0316970.0016060.0577190.0379830.0217890.4511880.1219010.0033580.4511880.2591820.1392920.70.0522260.0339040.0023950.0522260.0361300.0212510.5034150.1558050.0057530.5034150.2953120.1605430.80.0472560.0354030.0033260.0472560.0343680.0207260.5506710.1912080.0090800.5506710.3296800.1812690.90.0427590.0363100.0043790.0427590.0326920.0202150.5934300.2275180.0134590.5934300.3623720.20148410.0386900.0367230.0055290.0386900.0310970.0197150.6321210.2642410.0189880.6321210.3934690.2211991.10.0350080.0367300.0067540.0350080.0295810.0192290.6671290.3009710.0257420.6671290.4230500.2404281.20.0316770.0364020.0080270.0316770.0281380.0187540.6988060.3373730.0337690.6988060.4511880.2591821.30.0286620.0358040.0093260.0286620.0267660.0182910.7274680.3731770.0430950.7274680.4779540.2774731.40.0259350.0349900.0106300.0259350.0254600.0178390.7534030.4081670.0537250.7534030.5034150.2953121.50.0234670.0340070.0119170.0234670.0242190.0173990.7768700.4421750.0656420.7768700.5276330.3127111.60.0212340.0328940.0131710.0212340.0230380.0169690.7981030.4750690.0788130.7981030.5506710.3296801.70.0192130.0316850.0143760.0192130.0219140.0165500.8173160.5067540.0931890.8173160.5725850.3462301.80.0173850.0304090.0155190.0173850.0208450.0161420.8347010.5371630.1087080.8347010.5934300.3623721.90.0157300.0290880.0165890.0157300.0198290.0157430.8504310.5662510.1252980.8504310.6132590.37811520.0142330.0277430.0175790.0142330.0188620.0153540.8646650.5939940.1428770.8646650.6321210.3934692.10.0128790.0263910.0184810.0128790.0179420.0149750.8775440.6203850.1613570.8775440.6500620.4084452.20.0116530.0250450.0192900.0116530.0170670.0146060.8891970.6454300.1806480.8891970.6671290.4230502.30.0105440.0237160.0200050.0105440.0162340.0142450.8997410.6691460.2006530.8997410.6833630.4372952.40.0095410.0224130.0206240.0095410.0154430.0138930.9092820.6915590.2212770.9092820.6988060.4511882.50.0086330.0211440.0211470.0086330.0146890.0135500.9179150.7127030.2424240.9179150.7134950.4647392.60.0078110.0199130.0215740.0078110.0139730.0132160.9257260.7326150.2639980.9257260.7274680.4779542.70.0070680.0187240.0219090.0070680.0132920.0128890.9327940.7513400.2859080.9327940.7407600.4908442.80.0063950.0175820.0221550.0063950.0126430.0125710.9391900.7689220.3080630.9391900.7534030.5034152.90.0057870.0164880.0223140.0057870.0120270.0122610.9449770.7854090.3303770.9449770.7654300.51567530.0052360.0154420.0223920.0052360.0114400.0119580.9502130.8008520.3527680.9502130.7768700.5276333.10.0047380.0144470.0223920.0047380.0108820.0116630.9549510.8152980.3751600.9549510.7877520.5392963.20.0042870.0135000.0223200.0042870.0103510.0113750.9592380.8287990.3974800.9592380.7981030.5506713.30.0038790.0126040.0221820.0038790.0098470.0110940.9631170.8414020.4196620.9631170.8079500.5617653.40.0035100.0117550.0219810.0035100.0093660.0108200.9666270.8531580.4416430.9666270.8173160.5725853.50.0031760.0109540.0217240.0031760.0089100.0105530.9698030.8641120.4633670.9698030.8262260.5831383.60.0028740.0101990.0214170.0028740.0084750.0102920.9726760.8743110.4847840.9726760.8347010.5934303.70.0026000.0094890.0210630.0026000.0080620.0100380.9752760.8837990.5058470.9752760.8427630.6034693.80.0023530.0088210.0206680.0023530.0076690.0097900.9776290.8926200.5265150.9776290.8504310.6132593.90.0021290.0081940.0202380.0021290.0072950.0095490.9797580.9008150.5467530.9797580.8577260.62280840.0019260.0076070.0197770.0019260.0069390.0093130.9816840.9084220.5665300.9816840.8646650.6321214.10.0017430.0070580.0192890.0017430.0066000.0090830.9834270.9154790.5858180.9834270.8712650.6412044.20.0015770.0065440.0187780.0015770.0062780.0088590.9850040.9220230.6045970.9850040.8775440.6500624.30.0014270.0060640.0182490.0014270.0059720.0086400.9864310.9280870.6228460.9864310.8835160.6587024.40.0012910.0056160.0177060.0012910.0056810.0084270.9877230.9337020.6405520.9877230.8891970.6671294.50.0011680.0051980.0171520.0011680.0054040.0082190.9888910.9389010.6577040.9888910.8946010.6753484.60.0010570.0048090.0165900.0010570.0051400.0080160.9899480.9437100.6742940.9899480.8997410.6833634.70.0009570.0044470.0160230.0009570.0048900.0078180.9909050.9481570.6903160.9909050.9046310.6911814.80.0008660.0041110.0154540.0008660.0046510.0076250.9917700.9522670.7057700.9917700.9092820.6988064.90.0007830.0037980.0148850.0007830.0044240.0074370.9925530.9560650.7206550.9925530.9137060.70624250.0007090.0035070.0143190.0007090.0042090.0072530.9932620.9595720.7349740.9932620.9179150.7134955.10.0006410.0032380.0137580.0006410.0040030.0070740.9939030.9628100.7487320.9939030.9219180.7205695.20.0005800.0029870.0132030.0005800.0038080.0068990.9944830.9657970.7619350.9944830.9257260.7274685.30.0005250.0027560.0126560.0005250.0036220.0067290.9950080.9685530.7745900.9950080.9293490.7341975.40.0004750.0025410.0121190.0004750.0034460.0065630.9954830.9710940.7867090.9954830.9327940.7407605.50.0004300.0023420.0115920.0004300.0032780.0064010.9959130.9734360.7983010.9959130.9360720.7471605.60.0003890.0021580.0110770.0003890.0031180.0062430.9963020.9755940.8093780.9963020.9391900.7534035.70.0003520.0019880.0105740.0003520.0029660.0060890.9966540.9775820.8199520.9966540.9421560.7594925.80.0003180.0018310.0100850.0003180.0028210.0059380.9969720.9794130.8300370.9969720.9449770.7654305.90.0002880.0016850.0096100.0002880.0026840.0057920.9972610.9810980.8396470.9972610.9476600.77122160.0002610.0015510.0091490.0002610.0025530.0056490.9975210.9826490.8487960.9975210.9502130.7768706.10.0002360.0014270.0087030.0002360.0024280.0055090.9977570.9840760.8574990.9977570.9526410.7823796.20.0002130.0013120.0082720.0002130.0023100.0053730.9979710.9853880.8657710.9979710.9549510.7877526.30.0001930.0012070.0078560.0001930.0021970.0052400.9981640.9865950.8736260.9981640.9571480.7929926.40.0001750.0011100.0074550.0001750.0020900.0051110.9983380.9877040.8810810.9983380.9592380.7981036.50.0001580.0010200.0070690.0001580.0019880.0049850.9984970.9887240.8881500.9984970.9612260.8030886.60.0001430.0009370.0066990.0001430.0018910.0048620.9986400.9896610.8948490.9986400.9631170.8079506.70.0001290.0008610.0063430.0001290.0017990.0047420.9987690.9905220.9011920.9987690.9649160.8126926.80.0001170.0007910.0060020.0001170.0017110.0046250.9988860.9913130.9071940.9988860.9666270.8173166.90.0001060.0007260.0056760.0001060.0016280.0045100.9989920.9920380.9128700.9989920.9682540.82182770.0000960.0006660.0053640.0000960.0015480.0043990.9990880.9927050.9182350.9990880.9698030.8262267.10.0000870.0006120.0050660.0000870.0014730.0042900.9991750.9933170.9233010.9991750.9712750.8305177.20.0000790.0005610.0047820.0000790.0014010.0041850.9992530.9938780.9280830.9992530.9726760.8347017.30.0000710.0005150.0045110.0000710.0013330.0040810.9993240.9943930.9325940.9993240.9740090.8387827.40.0000640.0004720.0042530.0000640.0012680.0039800.9993890.9948650.9368470.9993890.9752760.8427637.50.0000580.0004330.0040080.0000580.0012060.0038820.9994470.9952990.9408550.9994470.9764820.8466457.60.0000530.0003970.0037740.0000530.0011470.0037860.9995000.9956960.9446290.9995000.9776290.8504317.70.0000480.0003640.0035530.0000480.0010910.0036930.9995470.9960600.9481810.9995470.9787200.8541247.80.0000430.0003340.0033420.0000430.0010380.0036020.9995900.9963940.9515230.9995900.9797580.8577267.90.0000390.0003060.0031430.0000390.0009870.0035130.9996290.9967000.9546660.9996290.9807450.86123980.0000350.0002800.0029540.0000350.0009390.0034260.9996650.9969810.9576200.9996650.9816840.8646658.10.0000320.0002570.0027750.0000320.0008930.0033410.9996960.9972380.9603950.9996960.9825780.8680068.20.0000290.0002350.0026050.0000290.0008500.0032590.9997250.9974730.9630000.9997250.9834270.8712658.30.0000260.0002160.0024450.0000260.0008080.0031780.9997510.9976890.9654460.9997510.9842360.8744448.40.0000240.0001970.0022940.0000240.0007690.0031000.9997750.9978860.9677400.9997750.9850040.8775448.50.0000210.0001810.0021510.0000210.0007310.0030230.9997970.9980670.9698910.9997970.9857360.8805678.60.0000190.0001660.0020160.0000190.0006960.0029490.9998160.9982330.9719070.9998160.9864310.8835168.70.0000180.0001520.0018890.0000180.0006620.0028760.9998330.9983840.9737970.9998330.9870930.8863928.80.0000160.0001390.0017700.0000160.0006290.0028050.9998490.9985230.9755660.9998490.9877230.8891978.90.0000140.0001270.0016570.0000140.0005990.0027360.9998640.9986500.9772230.9998640.9883210.89193390.0000130.0001160.0015500.0000130.0005700.0026680.9998770.9987660.9787740.9998770.9888910.8946019.10.0000120.0001060.0014500.0000120.0005420.0026020.9998880.9988720.9802240.9998880.9894330.8972039.20.0000110.0000970.0013560.0000110.0005150.0025380.9998990.9989690.9815800.9998990.9899480.8997419.30.0000100.0000890.0012680.0000100.0004900.0024750.9999090.9990580.9828480.9999090.9904380.9022179.40.0000090.0000810.0011850.0000090.0004660.0024140.9999170.9991400.9840330.9999170.9909050.9046319.50.0000080.0000740.0011070.0000080.0004440.0023550.9999250.9992140.9851400.9999250.9913480.9069869.60.0000070.0000680.0010340.0000070.0004220.0022970.9999320.9992820.9861740.9999320.9917700.9092829.70.0000060.0000620.0009650.0000060.0004010.0022400.9999390.9993440.9871390.9999390.9921720.9115229.80.0000060.0000570.0009010.0000060.0003820.0021850.9999450.9994010.9880400.9999450.9925530.9137069.90.0000050.0000520.0008400.0000050.0003630.0021310.9999500.9994530.9888800.9999500.9929170.915837100.0000050.0000480.0007840.0000050.0003450.0020780.9999550.9995010.9896640.9999550.9932620.917915

IC Media

=1 y =1=2 y =1=4 y =1Xf(X)Densidad Gamma

IC Medias

=1 y =1=1 y =2=1 y =4Xf(X)Densidad Exponencial

IC Varianza

=1 y =1=2 y =1=4 y =1XF(X)Funcin de Distribucin Gamma

PH Media

=1 y =1=1 y =2=1 y =4XF(X)Funcin de Distribucin Exponencial

PH MediasDistribucin Beta=2 y =2=3 y =3=5 y =3=2 y =2=3 y =3=5 y =3XF(X)F(X)F(X)f(X)f(X)f(X)00.0000000.0000000.0000000.0000000.0000000.0000000.010.0002980.0000100.0000000.0002980.0000100.0000000.020.0011840.0000780.0000000.0008860.0000680.0000000.030.0026460.0002580.0000000.0014620.0001800.0000000.040.0046720.0006020.0000020.0020260.0003440.0000020.050.0072500.0011580.0000060.0025780.0005560.0000040.060.0103680.0019700.0000150.0031180.0008120.0000090.070.0140140.0030800.0000310.0036460.0011100.0000170.080.0181760.0045250.0000600.0041620.0014450.0000290.090.0228420.0063410.0001060.0046660.0018160.0000460.10.0280000.0085600.0001770.0051580.0022190.0000700.110.0336380.0112100.0002790.0056380.0026500.0001030.120.0397440.0143190.0004230.0061060.0031080.0001440.130.0463060.0179090.0006200.0065620.0035900.0001970.140.0533120.0220000.0008820.0070060.0040920.0002620.150.0607500.0266120.0012220.0074380.0046120.0003400.160.0686080.0317590.0016550.0078580.0051470.0004330.170.0768740.0374540.0021980.0082660.0056950.0005430.180.0855360.0437070.0028690.0086620.0062540.0006710.190.0945820.0505280.0036870.0090460.0068200.0008180.20.1040000.0579200.0046720.0094180.0073920.0009850.210.1137780.0658880.0058450.0097780.0079680.0011730.220.1239040.0744340.0072280.0101260.0085450.0013840.230.1343660.0835560.0088460.0104620.0091220.0016170.240.1451520.0932510.0107210.0107860.0096960.0018750.250.1562500.1035160.0128780.0110980.0102640.0021580.260.1676480.1143420.0153440.0113980.0108270.0024650.270.1793340.1257230.0181420.0116860.0113810.0027980.280.1912960.1376480.0213000.0119620.0119250.0031580.290.2035220.1501050.0248420.0122260.0124570.0035430.30.2160000.1630800.0287960.0124780.0129750.0039530.310.2287180.1765590.0331850.0127180.0134790.0043900.320.2416640.1905260.0380370.0129460.0139670.0048520.330.2548260.2049630.0433760.0131620.0144370.0053380.340.2681920.2198510.0492250.0133660.0148880.0058490.350.2817500.2351690.0556080.0135580.0153190.0063830.360.2954880.2508970.0625460.0137380.0157280.0069390.370.3093940.2670120.0700620.0139060.0161150.0075150.380.3234560.2834910.0781730.0140620.0164780.0081120.390.3376620.3003080.0868990.0142060.0168180.0087260.40.3520000.3174400.0962560.0143380.0171320.0093570.410.3664580.3348600.1062580.0144580.0174200.0100020.420.3810240.3525400.1169160.0145660.0176810.0106590.430.3956860.3704550.1282430.0146620.0179150.0113260.440.4104320.3885750.1402450.0147460.0181200.0120020.450.4252500.4068730.1529280.0148180.0182980.0126830.460.4401280.4253190.1662950.0148780.0184460.0133670.470.4550540.4438850.1803450.0149260.0185650.0140510.480.4700160.4625400.1950780.0149620.0186550.0147320.490.4850020.4812550.2104860.0149860.0187150.0154090.50.5000000.5000000.2265630.0149980.0187450.0160760.510.5149980.5187450.2432950.0149980.0187450.0167320.520.5299840.5374600.2606680.0149860.0187150.0173730.530.5449460.5561150.2786650.0149620.0186550.0179970.540.5598720.5746810.2972630.0149260.0185650.0185990.550.5747500.5931270.3164400.0148780.0184460.0191770.560.5895680.6114250.3361670.0148180.0182980.0197270.570.6043140.6295450.3564120.0147460.0181200.0202460.580.6189760.6474600.3771430.0146620.0179150.0207300.590.6335420.6651400.3983200.0145660.0176810.0211770.60.6480000.6825600.4199040.0144580.0174200.0215840.610.6623380.6996920.4418510.0143380.0171320.0219470.620.6765440.7165090.4641130.0142060.0168180.0222620.630.6906060.7329880.4866410.0140620.0164780.0225280.640.7045120.7491030.5093830.0139060.0161150.0227420.650.7182500.7648310.5322830.0137380.0157280.0229000.660.7318080.7801490.5552840.0135580.0153190.0230010.670.7451740.7950370.5783260.0133660.0148880.0230420.680.7583360.8094740.6013470.0131620.0144370.0230210.690.7712820.8234410.6242830.0129460.0139670.0229360.70.7840000.8369200.6470690.0127180.0134790.0227860.710.7964780.8498950.6696400.0124780.0129750.0225700.720.8087040.8623520.6919270.0122260.0124570.0222870.730.8206660.8742770.7138620.0119620.0119250.0219360.740.8323520.8856580.7353790.0116860.0113810.0215170.750.8437500.8964840.7564090.0113980.0108270.0210300.760.8548480.9067490.7768850.0110980.0102640.0204760.770.8656340.9164440.7967420.0107860.0096960.0198570.780.8760960.9255660.8159150.0104620.0091220.0191740.790.8862220.9341120.8343440.0101260.0085450.0184280.80.8960000.9420800.8519680.0097780.0079680.0176240.810.9054180.9494720.8687320.0094180.0073920.0167640.820.9144640.9562930.8845850.0090460.0068200.0158530.830.9231260.9625460.8994800.0086620.0062540.0148950.840.9313920.9682410.9133750.0082660.0056950.0138950.850.9392500.9733880.9262350.0078580.0051470.0128600.860.9466880.9780000.9380310.0074380.0046120.0117970.870.9536940.9820910.9487440.0070060.0040920.0107130.880.9602560.9856810.9583610.0065620.0035900.0096170.890.9663620.9887900.9668800.0061060.0031080.0085190.90.9720000.9914400.9743080.0056380.0026500.0074290.910.9771580.9936590.9806670.0051580.0022190.0063580.920.9818240.9954750.9859860.0046660.0018160.0053190.930.9859860.9969200.9903120.0041620.0014450.0043260.940.9896320.9980300.9937060.0036460.0011100.0033940.950.9927500.9988420.9962430.0031180.0008120.0025370.960.9953280.9993980.9980160.0025780.0005560.0017730.970.9973540.9997420.9991370.0020260.0003440.0011210.980.9988160.9999220.9997360.0014620.0001800.0005990.990.9997020.9999900.9999660.0008860.0000680.00023011.0000001.0000001.0000000.0002980.0000100.000034

PH Medias

=2 y =2=3 y =3=5 y =3Xf(X)Densidad Beta

PH Varianza

=2 y =2=3 y =3=5 y =3XF(X)Funcin de Distribucin Beta

PH VarianzasDistribucin Normal=5 y =9=0 y =1Xf(X)F(X)Xf(X)F(X)-270.0000800.000189-3.0000.0013500.001350-260.0001180.000286-2.7500.0016300.002980-250.0001710.000429-2.5000.0032300.006210-240.0002470.000636-2.2500.0060150.012224-230.0003510.000932-2.0000.0105260.022750-220.0004920.001350-1.7500.0173090.040059-210.0006830.001933-1.5000.0267480.066807-200.0009360.002737-1.2500.0388430.105650-190.0012660.003830-1.0000.0530050.158655-180.0016920.005301-0.7500.0679720.226627-170.0022340.007254-0.5000.0819100.308538-160.0029140.009815-0.2500.0927560.401294-150.0037530.0131340.0000.0987060.500000-140.0047740.0173810.2500.0987060.598706-130.0059990.0227500.5000.0927560.691462-120.0074460.0294530.7500.0819100.773373-110.0091280.0377201.0000.0679720.841345-100.0110530.0477901.2500.0530050.894350-90.0132200.0599071.5000.0388430.933193-80.0156170.0743071.7500.0267480.959941-70.0182230.0912112.0000.0173090.977250-60.0210030.1108122.2500.0105260.987776-50.0239100.1332602.5000.0060150.993790-40.0268860.1586552.7500.0032300.997020-30.0298600.1870313.0000.0016300.998650-20.0327570.218350-10.0354940.25249300.0379880.28925710.0401580.32836120.0419310.36944130.0432460.41207040.0440540.45576450.0443270.50000060.0440540.54423670.0432460.58793080.0419310.63055990.0401580.671639100.0379880.710743110.0354940.747507120.0327570.781650130.0298600.812969140.0268860.841345150.0239100.866740160.0210030.889188170.0182230.908789180.0156170.925693190.0132200.940093200.0110530.952210210.0091280.962280220.0074460.970547230.0059990.977250240.0047740.982619250.0037530.986866260.0029140.990185270.0022340.992746280.0016920.994699290.0012660.996170300.0009360.997263

PH Varianzas

=5 y =9Xf(x)Densidad Normal =5 y =9

Simulacin Uniforme

=0 y =1Xf(x)Densidad Normal Estndar =0 y =1

Simulacin Binomial

XF(X)Distribucin Acumulada Normal Estndar =0 y =1

Simulacin Normal

XF(X)Distribucin Acumulada Normal =5 y =9

MonteCarloDistribucin Log-Normal=1 y =0.3=1 y =0.5Xf(X)F(X)f(X)F(X)0.100.00000000000000000000000000017360.00000000000000000000000000017360.000000000019853047047539780.000000000019853047047539780.200.00000000000000000168704332588130.00000000000000000168704332605490.000000089986345316615940000.000000090006198363663480000.300.00000000000010167261311678002000.00000000000010167430016010607000.000005127780922673158000000.000005217787121036821000000.400.00000000008413333145423506000000.00000000008423500575439516000000.000058185006915012494000000.000063402794036049310000000.500.00000000823147278256129400000000.00000000831570778831569000000000.000290813950629909000000000.000354216744665958000000000.600.00000022925859600221456000000000.00000023757430379053026000000000.000902783309555844000000000.001257000054221800000000000.700.00000282171507203802500000000000.00000305928937582855550000000000.002073336843509970000000000.003330336897731770000000000.800.00001973672535693360400000000000.00002279601473276216000000000000.003886463746949900000000000.007216800644681660000000000.900.00009176423271661793000000000000.00011456024744938000000000000000.006310779964445400000000000.013527580609127100000000001.000.00031450008574751600000000000000.00042906033319689600000000000000.009222551339052250000000000.022750131948179300000000001.100.00085315801202767700000000000000.00128221834522457000000000000000.012445890024549400000000000.035196021972728800000000001.200.00192706861610592000000000000000.00320928696133049000000000000000.015791105426551900000000000.050987127399280700000000001.300.00376110163681764000000000000000.00697038859814814000000000000000.019082659199085400000000000.070069786598366000000000001.400.00652126481300119000000000000000.01349165341114930000000000000000.022175371080483600000000000.092245157678849700000000001.500.01026011457159740000000000000000.02375176798274670000000000000000.024960946089625200000000000.117206103768475000000000001.600.01489128008602060000000000000000.03864304806876730000000000000000.027367846988173600000000000.144573950756648000000000001.700.02019854292393030000000000000000.05884159099269760000000000000000.029357276608973900000000000.173931227365622000000000001.800.02587235060566170000000000000000.08471394159835930000000000000000.030917355624281000000000000.204848582989903000000000001.900.03156017741490510000000000000000.11627411901326400000000000000000.032056879510415000000000000.236905462500318000000000002.000.03691698616876380000000000000000.15319110518202800000000000000000.032799468234591300000000000.269704930734910000000000002.100.04164585811984980000000000000000.19483696330187800000000000000000.033178514926432200000000000.302883445661342000000000002.200.04552393129819450000000000000000.24036089460007300000000000000000.033233075457741900000000000.336116521119084000000000002.300.04841320860310970000000000000000.28877410320318200000000000000000.033004684592737100000000000.369121205711821000000000002.400.05025870605052170000000000000000.33903280925370400000000000000000.032535002613619700000000000.401656208325441000000000002.500.05107774882889200000000000000000.39011055808259600000000000000000.031864162269220500000000000.433520370594661000000000002.600.05094435019133760000000000000000.44105490827393400000000000000000.031029680190840200000000000.464550050785501000000000002.700.04997200489248670000000000000000.49102691316642000000000000000000.030065806544536700000000000.494615857330038000000000002.800.04829731457062210000000000000000.53932422773704200000000000000000.029003203374793900000000000.523619060704832000000000002.900.04606592917547460000000000000000.58539015691251700000000000000000.027868860899152500000000000.551487921603985000000000003.000.04342149935412270000000000000000.62881165626664000000000000000000.026686179198889000000000000.578174100802874000000000003.100.04049775306909150000000000000000.66930940933573100000000000000000.025475158970625000000000000.603649259773499000000000003.200.03741343528633080000000000000000.70672284462206200000000000000000.024252658747354100000000000.627901918520853000000000003.300.03426964886785920000000000000000.74099249348992100000000000000000.023032687226562800000000000.650934605747415000000000003.400.03114906281039250000000000000000.77214155630031400000000000000000.021826708262974700000000000.672761314010390000000000003.500.02811646696038590000000000000000.80025802326070000000000000000000.020643943003932200000000000.693405257014322000000000003.600.02522021409289190000000000000000.82547823735359200000000000000000.019491658902177500000000000.712896915916500000000000003.700.02249417394871340000000000000000.84797241130230500000000000000000.018375439252671400000000000.731272355169171000000000003.800.01995991152353330000000000000000.86793232282583800000000000000000.017299429749460100000000000.748571784918631000000000003.900.01762888287027030000000000000000.88556120569610900000000000000000.016266560584510000000000000.764838345503141000000000004.000.01550451052594750000000000000000.90106571622205600000000000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MonteCarlo

=1 y =0.3=1 y =0.5Xf(X)Densidad Log-Normal

=1 y =0.3=1 y =0.5Xf(X)Distribucin acumulativa Log-Normal

Intervalo de Confianza para la MediaEjemplo 8.11 de Wackerly, Mendenhall III y Scheaffer, 6a.ed., pgina 401.Estadstica Matemtica con AplicacionesThomsoniX desconocida13005S=39.122995t inf.-2.36532925t sup.2.36543005cota inf.2926.352935cota sup.2991.7629377296582905

Intervalo de Confianza para MediasEjemplo 8.12 de Wackerly, Mendenhall III y Scheaffer, 6a.ed., pgina 403.Estadstica Matemtica con AplicacionesiX1X21 y 2 desconocidas13235Sp=4.71623731t inf.-2.12033529t sup.2.12042825cota inf.-1.0554134cota sup.8.3864440735278313293431Promedio35.2231.56Varianza24.4420.03

Intervalo de Confianza para la VarianzaEjemplo 8.13 de Wackerly, Mendenhall III y Scheaffer, 6a.ed., pgina 409.Estadstica Matemtica con AplicacionesThomsonX sigue unaiXdistribucin normal14.1S2=10.5725.22 inf.5.991310.22 sup.0.103cota inf.3.53cota sup.206.07

Prueba de Hiptesis para la MediaEjemplo 10.5 de Mendenhall, Scheaffer y Wackerly, 2a.ed., pgina 407.Estadstica Matemtica con AplicacionesIberoamrica1515n=36promedio=17varianza=9 conocida95% de confianzaZ=4.0z sup.1.645El estadstico de prueba supera en valor absoluto al estadstico tericoRechazar Ho

Prueba de Hiptesis para MediasEjemplo 10.7 de Mendenhall, Scheaffer y Wackerly, 2a.ed., pgina 410Estadstica Matemtica con AplicacionesIberoamricaEstadsticosn1=50n2=50promedio x1=3.6promedio x2=3.8varianza x1=0.18varianza x2=0.14muestra grande n>30S2=295% de confianzaZ=-2.500z inf.-2.576z sup.1.960El estadstico de prueba supera en valor absoluto al estadstico tericoRechazar Ho

Prueba de Hiptesis para la VarianzaEjemplo 10.16 de Mendenhall, Scheaffer y Wackerly, 2a.ed., pgina 434Estadstica Matemtica con AplicacionesIberoamrica0.00020.0002Estadsticosn1=10varianza x1=0.0003Las observaciones se distribuyen normal95% de confianzaX2=13.5X2 terica=16.919El estadstico de prueba NO supera en valor absoluto al estadstico tericoNo Rechazar Ho

Prueba de Hiptesis para la VarianzasEjemplo 10.19 de Mendenhall, Scheaffer y Wackerly, 2a.ed., pgina 436Estadstica Matemtica con AplicacionesIberoamricaEstadsticosn1=10n2=20varianza x1=0.0003varianza x2=0.0001Las observaciones se distribuyen normal95% de confianzaF=3.0F terica=2.42El estadstico de prueba supera en valor absoluto al estadstico terico

SimulacinDistribucin Uniformea =3b =8iXf(X)17.39586343980.225.68254872930.236.26900902390.246.53214628130.253.47561724180.265.99589605880.277.40890962970.283.85139863020.295.58584174350.2105.9401513230.2113.41602251190.2124.43731674570.2137.44603156560.2143.04292952820.2155.98102917480.2167.50853474560.2175.49694193850.2185.65222996830.2194.53852360030.2207.91648416390.2216.80855743370.2226.19381009260.2236.48003158140.2245.59167426240.2255.35653968410.2266.82994702570.2275.19270339670.2283.38113708660.2293.85006497210.2305.96704722210.2315.70584327570.2324.55990219790.2337.54237900160.2347.92108655940.2354.66272486650.2365.77203017450.2376.30913144260.2383.74340400330.2395.99282597010.2406.41784314810.2417.29360668080.2425.03824463270.2437.0661612740.2444.58176936760.2456.78245600250.2464.24517128940.2474.56803852440.2485.47694214430.2493.58183605130.2505.02297392510.2517.07129281690.2525.77728317860.2537.42523653710.2545.28243473920.2557.28411526090.2565.46074359930.2577.48028062360.2586.27806403160.2597.76169675170.2605.51961204650.2617.30731540310.2627.69743118620.2633.97797780.2645.93389927460.2655.15141194470.2667.8690565480.2675.43185045750.2684.00752232750.2695.45603352120.2706.35716625250.2716.46705281120.2723.34907170970.2733.05956541440.2747.35158045180.2753.60555215210.2763.74864243270.2774.00574369590.2783.43945875090.2793.00665775830.2807.83088363140.2816.77141643840.2823.23504486930.2836.62401344120.2847.40821940170.2854.29237346570.2867.1045910090.2877.5697063260.2883.64407420110.2896.00492901470.2906.5554936130.2917.43160230310.2923.77071892530.2936.26246673070.2945.42081484550.2955.20014650330.2967.39263206630.2977.38230915880.2984.79978062990.2995.91531618630.21005.04563020660.2

Xf(X)Simulacin Uniforme

SimulacinDistribucin Binomialn =50p =0.4Datos AgrupadosiXf(X)Intervalo XFrecuencia1210.1091033836002190.1108631156503190.11086311561014150.041546672515145170.080785196520406220.095878731125387170.08078519653068250.04046360363519170.080785196540010170.080785196545011200.114558552850012160.060588897413210.109103383614190.110863115615310.000854460516140.025966670317150.041546672518260.025938207419160.060588897420230.077814622321280.008417337222150.041546672523120.007562838924180.098737462425230.077814622326250.040463603627140.025966670328220.095878731129210.109103383630200.114558552831210.109103383632210.109103383633190.110863115634210.109103383635160.060588897436220.095878731137160.060588897438160.06058889743980.000169320140260.025938207441160.060588897442140.025966670343230.077814622344210.109103383645200.114558552846260.025938207447140.025966670348150.041546672549190.110863115650240.058360966751220.095878731152180.098737462453190.110863115654190.110863115655250.040463603656240.058360966757240.058360966758240.058360966759290.004257044160200.114558552861110.00349054162170.080785196563200.114558552864220.095878731165240.058360966766200.114558552867140.025966670368220.095878731169270.015370789670200.114558552871180.098737462472220.095878731173180.098737462474220.095878731175170.080785196576200.114558552877230.077814622378210.109103383679160.060588897480250.040463603681220.095878731182170.080785196583210.109103383684240.058360966785220.095878731186180.098737462487200.114558552888200.114558552889170.080785196590240.058360966791230.077814622392130.014737839993140.025966670394210.109103383695210.109103383696180.098737462497140.025966670398180.098737462499200.1145585528100250.0404636036

f(X)Xf(X)Funcin de probabilidadBinomial n=50, p=0.4

FrecuenciaXFrecuenciaHistograma de FrecuenciaDistribucin Binomialn=50, p=0.4

SimulacinDistribucin Normalmedia =3varianza =9iXf(X)11.43821626510.11612824022-1.39188445880.045540991934.14858765140.1235829547.22915893510.049232290556.9569471140.055720449163.56363307510.130654370574.84385613960.110093100585.05770435250.105106493290.38912424530.0910583442105.54428535330.0928116149110.87150503490.103390235412-0.9291348270.0564035561134.80783061560.1109006691142.66430630020.1321508254152.80170282930.1326905751163.60399354490.130312750617-2.09101376390.031509597218-1.53720193370.0423736456191.75726317150.1220468204201.58465540650.1189752574215.19466125770.1017601945226.99512078890.0547886351234.64869747920.1143419086248.17790202930.0299857666257.61983032210.0406293843261.99587991230.1257367167274.09815586980.1243633397287.43329080350.0446257848295.80663229810.0858484108303.90917313770.1270121141312.57136416650.131630309632-4.59140419220.0054117372330.62918315890.097313655340.61240682320.0968830317355.41719649690.0961204695363.45874515150.1314350681373.81353850170.1281799706385.45350334530.0951807642394.4919336880.1175125607400.83652460420.1025314613410.6365723090.0975029628420.73545972440.1000137466438.81648763740.0203011006444.2323546140.1222211797456.77208092690.060323816464.06040515430.124927617347-0.18824440670.0756023719485.16577929230.1024746623496.9323358640.0563247563504.95007617120.1076556764514.27036205930.1215769996520.44626879360.0925636493533.16294028980.132784761554-0.62250790890.0641467321554.45915197360.1181458365565.21222923550.1013234516574.81496980590.110741432458-1.44158164580.044443736459-2.06700876880.0319393573601.92245547870.1246735573614.22857885250.1222842886626.51428099410.066959224963-3.22352435490.015462418964-2.01151895380.0329472823652.70403092310.1323351763661.34118585450.1141295509670.1782069880.0854424003683.25168284390.1325136067690.73121214210.099906813170-0.99626034510.0547609232713.19283368690.1327063289721.27909689110.1128067595735.02680173060.1058461249742.70599712310.1323437049751.77489831990.1223422642763.14291052590.1328299612770.92683243560.1047341631786.68958318310.062422472279-0.79287303730.0597989783800.88826195870.103799165811.61968069210.1196242393822.74309593990.1324940591838.1344582580.0307414573841.02587826560.1070928008859.62318291360.0116251842864.87387128690.10941270787-1.43847022750.0445120089882.86518834530.1328465603892.45769417530.1308256881901.30672469690.1133994578910.51452172720.0943493453922.64495250120.1320527144936.9180676410.0566763497942.47409906870.1309531149950.2980239550.0886425968.64415981650.0226553647972.71041770970.132362673998-1.25254770970.0486926838996.42177118190.06938919991004.10593047470.1242450028

Xf(X)Simulacin Normal

Simulacin de MonteCarlo para Intervalo de Confianza en la Valuacin de una Opcin Europea* Desmond J. Higham (2004) An Introduction to Financial Option Valuation* Mathematics, Stochastics and Computation* Cambridge University PressS =4.0E =5.0sigma =0.3r =0.04T =1.0Dt =0.001N = T/Dt =1,000M =10,000STMedia0.9795014.409550.5672961918Desviacin Estndar0.2902523.350981.584360010433.894851.0618129503Intervalo de Confianza 95%44.309000.6639018593Cota Inferior0.9738154.271130.7002939169Cota Superior0.9851963.992170.968316334273.904981.052081050584.329540.644174542194.208650.7603174115104.103160.8616716026113.672851.2751121377123.578291.3659602767133.563161.3804973101143.949451.0093591748153.994020.9665377057163.953071.0058762056173.965910.9935382264184.024790.9369712133193.975010.9847968619204.045260.9173005357214.121760.8437990565223.566951.3768584212233.798631.1542658524244.010000.9511776439254.112050.8531345916263.772401.1794657617273.979210.9807623087284.270150.7012346936294.664040.3227847245303.447221.4918937862313.810761.1426091401323.927181.0307501893333.902711.0542602831344.277040.6946135391353.437391.5013375669363.487801.4529052164373.951431.0074560226383.317651.6163869697394.185640.7824312755404.315320.6578329481414.321370.6520227368423.792381.160268185434.196170.7723096279444.585680.3980722559453.836671.1177143291463.836601.1177858317474.308400.6644790312484.451570.5269210718493.902471.0544930783504.238140.7319825322514.062810.9004392606524.261890.709171595534.151520.8152095044544.378240.5973762772553.998460.9622727695564.266770.7044786984573.368351.5676675338583.448811.4903687997593.726611.2234603279603.814871.1386619898614.133080.8329319307623.659491.287947972633.945861.0128103212643.957521.0016068806653.734671.2157188901663.568341.3755200768674.401680.5748635821683.526651.4155812464694.167850.7995237601704.278600.6931115563714.295320.6770498155723.383991.5526414908734.046180.9164186925744.222800.7467298551753.703701.2454721243763.616761.3290068647774.192290.776042845783.811451.1419453639793.329701.6048107572803.803361.1497169079814.157540.8094224761824.419090.558131742833.937951.0204095193843.731171.2190776353854.100640.8640926222863.840611.1139328799873.306981.6266403882883.927711.0302476701893.417051.5208797643904.363880.6111814882913.715451.2341864505924.028060.9338341277934.200670.7679858111943.787891.1645793281953.983390.9767495627964.404530.5721231817973.905331.051751715984.131420.8345246903993.997560.96313262211003.742001.20866984671013.818981.13470865481024.151060.81565638481034.677100.31024247891043.382941.55365890671054.564120.41878674651064.806190.18621302871073.937061.02126398751084.162570.80459068691093.364271.57159626451103.676431.27167105071114.257580.71331140461124.123000.84261146581134.463220.51573659981143.952501.00642336491154.341300.63287423471164.194000.77440097061174.200080.7685517521184.178510.78927809691193.957321.00179900071203.321431.61274813161213.772071.17978361051224.228960.74080380451233.606181.33916365361243.647871.29911683031253.488871.45187926381264.198820.7697664451273.539251.40347401671283.683011.26535214111293.774551.1774013461303.933661.02452562211314.087380.87683465491323.613061.33255623471333.793591.15910999381343.840101.11441850051354.390400.58569576841364.335610.63833889941373.826951.12705839031384.017670.94381296821393.579591.36471012581403.875641.08026921971414.450310.52814052411424.172680.79488366161433.875221.08067251511444.050750.91202478751453.543451.39944255591463.998640.96209313481473.632081.31428185031483.776911.17512872351493.931101.02698894121503.356961.57861161361513.584181.36030095111524.207000.76190996961534.110640.85448326031544.289650.6824971621554.318840.65445495991563.495691.4453205221573.876001.07992447631584.031710.93032715551594.081900.88210518451604.115960.84937326921614.088720.87555052291623.863061.09236125341633.297901.63535571151643.943111.01544895341653.583821.36065285561664.426190.55131470161674.459000.51978907341683.721611.22826225891694.275230.69635230931704.381060.594669111713.891391.0651361251723.483511.45702446131734.430680.54699579241744.354830.61986944481754.493850.48630677911764.468160.51098607061774.111090.85405413291784.237610.73249727121793.979340.98063926451803.272181.66006968051813.777991.17409320011824.004510.95645567241833.565031.37870870031843.894551.06210239071854.110110.85499333771863.876001.07992483251873.810441.14292104551883.751011.20001656741894.009280.95187440991904.343890.63038000841913.907091.05005954341923.831541.12264880341933.905431.05165564171944.279400.69234934891953.784671.1676759751963.975290.98453295451974.805700.18668526441983.697381.25154375911994.358720.61613684362003.514421.42733052212014.256880.71398664352023.909591.04765897592034.490990.48904857122043.777851.17423080772053.956321.00275654512064.137580.82860873712073.348251.58698228212084.112800.8524086092094.007980.95312210992103.958231.00092538872113.794441.15829339782123.912921.04445400332134.176510.79120117092143.926901.03102526882154.633790.35185108012163.989290.97108408622174.040780.9216041712183.808181.14508561942194.283800.68811452922203.369561.56651003212213.916981.04055184122223.949741.00907530712234.155360.81151645652243.808871.14442962692253.506311.43512187832264.113800.8514485972273.537331.40531756552284.150950.81575587012294.411930.565012382303.782351.16990766952313.537331.40531614432323.779371.1727649172333.811531.14186646472344.066070.89730676872353.560541.38301858472363.888031.06836740622373.458721.4808471258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