Actividad-5 - Generación Manual de Variables Aleatorias

October 6, 2022 | Author: Anonymous | Category: N/A

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En las tres siguientes pestañas se encuentran 3 muestras de diferentes estudios. El estudiante deberá depurarlas, prepararlas, realizar las pruebas estadiscas respecvas para comprobar que son numeros aleatorios y de serlos encontrar la distribución de probabilidad adecuada para cada muestra. Por úlmo deberá generar 100 datos de la distribución correspondiente a cada muestra.

Actividad 5 - Generación manual de variables aleatorias German Mendoza Cruz Robert Orlando Angarita Zulma Cristina Barrera Rincón

Facultad de Ingeniería, Corporación Universitaría Iberoamericana

Modelamiento y simulación 06 de abril de 2022

Comprobar aleatoriedad de los datos CORRIDA DE LA MEDIA

#

MUESTRA 1

S

N° corridas

Media 29.42758804

56.748744226 47.8630779158 31.1212821346

1

1

1

0

N

1

0

alfa

20.2013174526 29.4099531156 35.2627186808 33.4811835621 30.315432471 33.6263084874 17.2620128916 36.5587686737 53.1655334162 26.8613120784

0

1

n1

0

0

n2

1

1

Valor esperado

1

0

Varianza

1

0

Estadisco

1

0

Valor en tabla

0

1

1

1

1

0

0

1

28.093509246 22.4369649823 28.1148913956 38.2369421845 11.9306884073 18.4288097055 35.5050659807 36.361724617 4.68006840567 25.4781228522

0

0

0

0

0

0

1

1

0

1

0

0

1

1

1

0

0

1

0

0

25.7492650782 52.2937829862 47.0362888979 29.0389764315 29.5336508374 61.5670323552 31.3625408011 35.787146249 16.4812306107 43.4012237235

0 1

0 1

1

0

0

1

1

1

1

0

1

0

1

0

0

1

33

1

1

34 35

3.87636916833 34.9621218415

0 1

1 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Co

Conclusión

36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74

25.3979291666 21.2751468276 57.1440648658 46.6267381401 1.48481326891 8.49097810718 18.1474695845 60.2981539052 48.3038243011 16.2098980369 13.5800266231 23.2894348347 49.4697166227 19.9575431086 1.18128698234 41.9772350553 4.9430357742 44.13973546 18.2565876916 15.7382920797 42.9859130008 38.5493274823 32.3509362324 18.9551120809 53.4864985469 37.5958641077 19.364280205

0

1

0

0

1

1

1

0

0

1

0

0

0

0

1

1

1

0

0

1

0

0

0

0

1

1

0

1

0

0

1

1

0

1

1

1

0

1

0

0

1

1

1

0

1

0

0

1

1

1

1

0

0

1

5.41703803534 24.8929173939 32.3204394025 26.8443463745 31.4828010686 19.2448036826 42.2610943983 9.19640425107 25.2996226347 8.63039418415

0

0

0

0

1

1

0

1

1

1

0

1

1

1

0

1

0

0

0

0

18.0913491504 19.2985824718

0

0

0

0

75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113

26.0668740437 45.514380215 39.7360424347 26.43368676 4.49292455491 48.5447917019 3.88249941816 40.8386118488 54.6673570022 78.2379523539 46.9066749209 2.52666995496 13.6481582488 9.3299550548 23.2117429163 41.3066135629 29.0022645605 38.3068898646 48.7724980428 63.1666562384 7.42803052681 34.5024893714 28.1248550543 34.5161537853 27.8709384616 47.324815161 5.92961661123

21.3624373524 28.7642614754 50.9681942533 34.4113353999 -4.74790432306 66.807242026 20.1009120141 33.7808328201 42.8107857188 26.5322114862

16.2338490297 19.4132186749

0

0

1

1

1

0

0

1

0

0

1

1

0

1

1

1

1

0

1

0

1

0

0

1

0

0

0

0

0

0

1

1

0

1

1

1

1

0

1

0

0

1

1

1

0

1

1

1

0

1

1

1

0

1

0

0

0

0

1

1

1

0

0

1

1

1

0

1

1

1

1

0

0

1

0

0

0

0

114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150

50.6605216909 41.0500650012 3.33980748615 44.0637360823 37.260886255 32.8583056837 21.5550909171 27.3029115489 22.0866716372 34.5188932005 10.9641166561 -9.21442586539 63.0934925717 32.8252457005 26.354552179 41.896430796 18.80067363 3.96290648742 35.8293045652 35.0576726667 38.2051999841 16.9541576283 27.3179013391 14.099021675 28.6940177857 -21.2296922525 35.2735037728

52.8691030709 32.2519671147 27.1913821174 27.7962976592 26.5690565624 17.3607185698 -2.31594165343 39.3011710826 67.9967327624 30.3955343928

1

1

1

0

0

1

1

1

1

0

1

0

0

1

0

0

0

0

1

1

0

1

0

0

1

1

1

0

0

1

1

1

0

1

0

0

1

1

1

0

1

0

0

1

0

0

0

0

0

0

0

0

1

1

1

0

1

0

0

1

0

0

0

0

0

0

0

0

1

1

1

0

1

0

Encontrar la distribición distribición de probabilidad d MUESTRA 1

75 150 0.05 78 72

75.880 37.128 12.164 1.960 No se acepta la hipotesis nula. Los datos no son independientes, por lo tanto la secuencia NO es aleatoria.

-21.22969 -9.214426 -4.747904 -2.315942

1.181287 1.4848133 2.52667 3.3398075 3.8763692 3.8824994 3.9629065 4.4929246 4.6800684 4.9430358 5.417038 5.9296166 7.4280305 8.4909781 8.6303942 9.1964043 9.3299551 10.964117 11.930688 13.580027 13.648158 14.099022 15.738292 16.209898 16.233849 16.481231 16.954158 17.262013 17.360719 18.091349 18.14747 18.256588

Promedio

Min

Max

Rango

n

# intervalos

Tamaño

1

2

3

4

5

6

7

8

60 50 40 30 20 10 0

2 -8.23

Co Con n lla a ayu ayu

18.42881 18.800674 18.955112 19.244804 19.298582 19.36428 19.413219 19.957543 20.100912 20.201317 21.275147 21.362437 21.555091 22.086672 22.436965 23.211743 23.289435 24.892917 25.299623 25.397929 25.478123 25.749265 26.066874 26.354552 26.433687 26.532211 26.569057 26.844346 26.861312 27.191382 27.302912 27.317901 27.796298 27.870938 28.093509 28.114891 28.124855 28.694018 28.764261

Signicancia

N

K-S

Xi

0

1

2

3

4

5

6

7

D+ es menor

Signicancia

N Chi Tabla

Xi

0

1

2

3

4

5

6

7

El ch chii-ca callcul cul los datos

29.002265 29.038976 29.409953 29.533651 30.315432 30.395534 31.121282 31.362541 31.482801 32.251967 32.320439 32.350936 32.825246 32.858306 33.481184 33.626308 33.780833 34.411335 34.502489 34.516154 34.518893 34.962122 35.057673 35.262719 35.273504 35.505066 35.787146 35.829305 36.361725 36.558769 37.260886 37.595864 38.2052 38.236942 38.30689 38.549327 39.301171 39.736042 40.838612

41.050065 41.306614 41.896431 41.977235 42.261094 42.810786 42.985913 43.401224 44.063736 44.139735 45.51438 46.626738 46.906675 47.036289 47.324815 47.863078 48.303824 48.544792 48.772498 49.469717 50.660522 50.968194 52.293783 52.869103 53.165533 53.486499 54.667357 56.748744 57.144065 60.298154 61.567032 63.093493 63.166656 66.807242 67.996733 78.237952

los datos

Generar 1

29.43 -21.23 78.24 99.47 150.00 8.18 13.000

Intervalos

Clase

Frecuencia

-21.23

-8.23

-8.23

2

-8

4.77

4.77

11

5

17.77

17.77

20

18

30.77

30.77

48

31

43.77

43.77

41

44

56.77

56.77

20

57

69.77

69.77

7

70

82.77

82.77

1

y mayor...

0

Hist ograma Muest ra 1 48 41

20

20

11

7 1

4.77

17.77

30.77

43.77

56.77

69.77

a visual se puede notar que el histograma se comporta como una distribución binomial.

82.77

K-S 0.05 150 0.1110

X

Fo

Fo Acum

F(X)

Fo Acum- F(x)

2

1%

0.013

0.015

0.002

11

7%

0.087

0.102

0.016

20

13%

0.220

0.316

0.096

48

32%

0.540

0.608

0.068

41

27%

0.813

0.847

0.034

20

13%

0.947

0.964

0.018

7

5%

0.993

0.996

0.003

1

1%

1.000

1.000

0.000

D+

0.096

a K-S entonces los datos se ajustan a una distribución binomial.

CHI-CUADRADO 0.05 150 11.0705

X

Fo

Fo Acum

F(X)

Ei

(Oi-Ei)^2/Ei

2

1%

0.013

0.015

2.284

0.035

11

7%

0.087

0.087

13.079

0.331

20

13%

0.220

0.214

32.103

4.563

48

32%

0.540

0.292

43.777

0.407

41

27%

0.813

0.239

35.818

0.750

20

13%

0.947

0.117

17.583

0.332

7

5%

0.993

0.032

4.795

1.013

1

1%

1.000

0.004

0.561

0.345

1.00 1.000 0

Chi calculado

150. 15 0.00 000 0

7.78

do es la Maxima desviación que permite la prueba chi - cuadrado para decir que corresponden a una distribución binomial. Chi-Calculado es menor al chi-tabla

0 numeros aleatorios con distribución binomial Promedio

25.5

Desv. Est

3.3

Este gráfico no está disponible en en su v

#

Ale Aleat. Unifor forme 1

Aleato. Binomial

0.409895 0.4098953030 30306 6 24.74821 24.748212796 27969343 9343

2 0.661143 0.661143314629 314629 26.8714320060833 26.8714320060833 3

0.058258 0.0582581818 18184 4 20.32043 20.320435744 57444097 4097

4 0.329676 0.329676031367 031367 24.0453338794215 24.0453338794215 5 0.147697 0.147697180922 180922 22.0470084863396 22.0470084863396 6 0.8 0.87834 78341183 1183517 517

29.3 29.35022 50223627 3627635 635

7 0.260146 0.260146002184 002184 23.3784453321709 23.3784453321709 8 0.575040 0.575040909085 909085 26.1244353107782 26.1244353107782 9 0.100269 0.100269432173 432173 21.2759411524057 21.2759411524057 10 0.52821 0.528212422 2422641 641

25.7 25.73356 33564442 4442199 199

11 0.45451 0.454519247 9247845 845

25.1 25.12297 22970331 0331581 581

12 0.803231530991 0.803231530991 28.3156282398979 28.3156282398979 13 0.058519364002 0.058519364002 20.3278272642517 20.3278272642517 14 0.716263472063 0.716263472063 27.3868641254683 27.3868641254683 15 0.338324542069 0.338324542069 24.1237677017914 24.1237677017914 16 0.555088527093 0.555088527093 25.9571432198203 25.9571432198203 17 0.461466428231 0.461466428231 25.1807579296969 25.1807579296969 18 0.951542923121 0.951542923121 30.9780049010745 30.9780049010745 19

0.956558 0.9565589580 95808 8 3 31.14 1.149861 98611829 1829648 648

20 0.77600 0.776005710 5710731 731

28.0 28.00394 03949692 9692704 704

21 0.900857299402 0.900857299402 29.7452912146648 29.7452912146648 22 0.960302331935 0.960302331935 31.2888774760452 31.2888774760452 23 0.259962576345 0.259962576345 23.3765794103853 23.3765794103853 24 0.977985760957 0.977985760957 32.1456046503547 32.1456046503547 25 0.497114118623 0.497114118623 25.4761281466732 25.4761281466732 26 0.298406249727 0.298406249727 23.7543335352907 23.7543335352907 27 0.212908271972 0.212908271972 22.8719763533914 22.8719763533914 28

0.4633 0.4633723 723234 234 25. 25.19 19659 659358 358144 14454 54

29 0.447980028095 0.447980028095 25.0684706821383 25.0684706821383 30 0.951119960995 0.951119960995 30.9641766493687 30.9641766493687 31 0.100825610935 0.100825610935 21.2863577356119 21.2863577356119 32 0.477506450693 0.477506450693 25.3138375160728 25.3138375160728

Si edita esta forma o guarda el libro en gráfico no se podrá utilizar.

33 0.832023806972 0.832023806972 28.6752387311072 28.6752387311072 34 0.324354528988 0.324354528988 23.9966641377758 23.9966641377758 35 0.094329251408 0.094329251408 21.1619586930165 21.1619586930165 36 0.926695044556 0.926695044556 30.2903149660502 30.2903149660502 37 0.123948403249 0.123948403249 21.6869392889724 21.6869392889724 38 0.567671934162 0.567671934162 26.0624855094893 26.0624855094893 39

0.241861 0.2418616700 67008 8 2 23.18 3.188922 89220966 0966721 721

40

0.122 0.122968 968440 44005 05

21. 21.671 671092 092665 665418 418

41 0.969143778294 0.969143778294 31.6655753296464 31.6655753296464 42 0.898358176349 0.898358176349 29.6984311342793 29.6984311342793 43 0.047581723296 0.047581723296 19.9930669276371 19.9930669276371 44 0.535788146981 0.535788146981 25.7964331944484 25.7964331944484 45 0.62073 0.620732547 2547916 916

26.5 26.51443 14437448 7448318 318

46 0.448482309963 0.448482309963 25.0726608230182 25.0726608230182 47

0.077830 0.0778307094 70946 6 2 20.81 0.814609 46090502 0502016 016

48 0.318423896426 0.318423896426 23.9420347705332 23.9420347705332 49 0.118297466034 0.118297466034 21.5943157383348 21.5943157383348 50 0.885932653348 0.885932653348 29.4770865460572 29.4770865460572 51 0.75229 0.752290837 0837956 956

27.7 27.74966 49663969 3969738 738

52 0.372695653202 0.372695653202 24.4284166317134 24.4284166317134 53

0.513383 0.5133839264 92643 3 2 25.61 5.610730 07309194 9194039 039

54 0.999073494735 0.999073494735 35.7723477701735 35.7723477701735 55 0.191446777652 0.191446777652 22.6204951363293 22.6204951363293 56 0.441772386661 0.441772386661 25.0166255986085 25.0166255986085 57 0.647632000209 0.647632000209 26.7504860917957 26.7504860917957 58 0.111153596525 0.111153596525 21.4726270087892 21.4726270087892 59 0.418533489659 0.418533489659 24.8213662429436 24.8213662429436 60 0.333703642837 0.333703642837 24.0819600728711 24.0819600728711 61 0.18749 0.187499530 9530397 397 62

22.5 22.57241 72410597 0597704 704

0.990651 0.9906516102 61025 5 3 33.26 3.260022 00228925 8925697 697

63 0.581643921995 0.581643921995 26.1801327154832 26.1801327154832 64 0.269830144328 0.269830144328 23.4760216220526 23.4760216220526 65 0.085959924523 0.085959924523 20.9919990266205 20.9919990266205 66

0.174250 0.1742501092 10929 9 2 22.40 2.406242 62422646 2646728 728

67 0.405731339323 0.405731339323 24.7128196323576 24.7128196323576 68 0.04955 0.049552263 2263789 789

20.0 20.05760 57605510 5510964 964

69 0.934323640504 0.934323640504 30.4790036188544 30.4790036188544 70 0.025120730772 0.025120730772 19.0389219478489 19.0389219478489 71 0.054432418685 0.054432418685 20.2090561767948 20.2090561767948

72 0.499427341639 0.499427341639 25.4952630409643 25.4952630409643 73

0.871722 0.8717222079 20792 2 2 29.24 9.244080 40805644 5644487 487

74 0.098947898503 0.098947898503 21.2510200332418 21.2510200332418 75 0.947346861059 0.947346861059 30.8448634949077 30.8448634949077 76

0.302719 0.3027193840 38404 4 2 23.79 3.795235 52358444 8444655 655

77 0.707706987027 0.707706987027 27.3041043726455 27.3041043726455 78 0.636782747775 0.636782747775 26.6545787294894 26.6545787294894 79 0.479401047777 0.479401047777 25.3295322936907 25.3295322936907 80 0.807950216076 0.807950216076 28.3722129542298 28.3722129542298 81 0.99214 0.992146074 6074425 425

33.4 33.47159 71591465 1465404 404

82 0.054870527581 0.054870527581 20.2221182470317 20.2221182470317 83 0.622930838898 0.622930838898 26.5335182827175 26.5335182827175 84 0.881571604532 0.881571604532 29.4035033184308 29.4035033184308 85 0.858065637722 0.858065637722 29.0365077355728 29.0365077355728 86 0.969210946686 0.969210946686 31.6687607607697 31.6687607607697 87 0.399287005313 0.399287005313 24.6578629859375 24.6578629859375 88 0.670608149472 0.670608149472 26.9572571246489 26.9572571246489 89 0.240271632857 0.240271632857 23.1720841071942 23.1720841071942 90 0.68707 0.687074892 4892758 758

27.1 27.10900 09000726 0726013 013

91 0.01106 0.011063502 3502403 403

17.9 17.94900 49003952 3952661 661

92 0.871401539309 0.871401539309 29.2390362010671 29.2390362010671 93 0.167785484469 0.167785484469 22.3222541708864 22.3222541708864 94 0.576639819881 0.576639819881 26.1379054486657 26.1379054486657 95 0.897247198909 0.897247198909 29.6778689476442 29.6778689476442 96 0.805848418037 0.805848418037 28.3469056104808 28.3469056104808 97 0.465913723495 0.465913723495 25.2176986990773 25.2176986990773 98 0.90359 0.903596325 6325239 239

29.7 29.79765 97652793 2793483 483

99 0.760660251476 0.760660251476 27.8378124663421 27.8378124663421 100 0.028467318288 0.028467318288 19.2174194742964 19.2174194742964

rsión de Excel. un formato de archivo diferente, el

Comprobar aleatoriedad de los datos CORRIDA DE LA MEDIA

#

MUESTRA 2

S

N° corridas

1 2 3

3 9 5

0 1 0

1 1 1

4 5 6

2 4 7

0 0 1

0 0 1

7 8 9 10 11 12 13 14 15 16

3 7 9 4 3 5 9 4 10 9

0 1 1 0 0 0 1 0 1 1

1 1 0 1 0 0 1 1 1 0

17 18

4 3

0 0

1 0

19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

8 4 6 3 2 9 10 4 3 8 3 10 1 4 8 4 9 7 5 7 10 4 9 8 9 7 6

1 0 1 0 0 1 1 0 0 1 0 1 0 0 1 0 1 1 0 1 1 0 1 1 1 1 1

1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 1 1 0 1 1 0 1 1 0 0 0 0

Media 5.54

Co N alfa n1 n2 Valor esperado Varianza Estadisco Valor en tabla

Conclusión

46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

6 2 9 3 6 5 8 4 6 2 10 7 7 6 8 3 3 2 4 8 3

1 0 1 0 1 0 1 0 1 0 1 1 1 1 1 0 0 0 0 1 0

0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 1 1

67 68 69 70 71 72 73 74 75 76 77 78 79

3 5 5 9 5 8 1 5 5 2 4 4 5

0 0 0 1 0 1 0 0 0 0 0 0 0

0 0 0 1 1 1 1 0 0 0 0 0 0

80 81 82 83 84 85 86 87 88 89 90 91 92

7 10 10 7 10 8 1 10 3 2 9 1 2

1 1 1 1 1 1 0 1 0 0 1 0 0

1 0 0 0 0 0 1 1 1 0 1 1 0

93 94 95

10 3 9

1 0 1

1 1 1

96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116

8 10 5 8 5 7 8 3 1 6 5 7 4 5 5 1 6 7 1 8 2

1 1 0 1 0 1 1 0 0 1 0 1 0 0 0 0 1 1 0 1 0

0 0 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 0 1 1 1

117 118 119 120 121 122 123 124 125 126 127 128 129

6 8 7 1 1 10 1 4 8 2 1 8 6

1 1 1 0 0 1 0 0 1 0 0 1 1

1 0 0 1 0 1 1 0 1 1 0 1 0

130 131 132 133 134 135 136 137 138 139 140 141 142

1 4 10 10 5 6 2 3 10 2 5 8 9

0 0 1 1 0 1 0 0 1 0 0 1 1

1 0 1 0 1 1 1 0 1 1 0 1 0

143 144 145

2 1 2

0 0 0

1 0 0

146 147 148 149 150

6 9 2 8 8

1 1 0 1 1

1 0 1 1 0

Encontrar lla ad diistribición d de ep prro MUESTRA 2 1 86 150 0.05

1 1 1

77 73 75.947

1 1 1

37.195 12.142 1.960

1 1 1 1 1 1 2 2 2 2

No se acepta la hipotesis nula. Los datos no son independientes, por lo tanto la secuencia NO es aleatoria.

2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4

4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7

7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10

10 10 10 10

babilidad de los datos

Promedio

5.54

Min Max Rango

1.00 10.00 10.00

n # intervalos Tamaño

2.00 3. 3.0 00 3.400

Clase 1 2 3 4 5 6 7 8

Fre Frecue uen ncia 13 15 16 16 17 12 13 19

9 10

14 15

4 2

0

0

y mayor...

Histograma muestra 2 19

20 18 15

16 14

16

16

17

13

13

12

12

14

15

10 8 6

1

2

3

4

5

6

7

8

9

10 10

Con la ayuda visual se puede notar que los datos enen una distribución uniforme

CHI-CUADRADO Signicancia N Chi Tabla Xi 1 2 3 4 5 6 7 8 9 10

0.05 150 15.5073 X 13 15 16 16 17 12 13 19 14 15

Fo 9% 10% 11% 11% 11% 8% 9% 13% 9% 10%

Ei 15.000 15.000 15.000 15.000 15.000 15.000 15.000 15.000 15.000 15.000 Chi calculado

(Oi-Ei)^2/Ei 0.267 0.000 0.067 0.067 0.267 0.600 0.267 1.067 0.067 0.000 2.67

El chi-calculado es la Maxima desviación que permite la prueba chi - cuadrado para decir que los datos corresponden a una distribución Uniforme. Chi-Calculado es menor al chi-tabla entonces los datos se

Generar 100 numeros aleatorios con distribución exponencial LI

5

LS

10

#

Alea Aleat. t. Unif Unifor orme me

Alea Aleato to.. Un Unif ifor orme me

1 2 3

0.932 0.011 0.127

9.318 0.109 1.273

4 5 6 7 8 9 10 11 12 13

0.629 0.308 0.559 0.501 0.740 0.454 0.445 0.241 0.357 0.590

6.286 3.075 5.587 5.009 7.404 4.535 4.449 2.412 3.565 5.905

14 15

0.670 0.839

6.703 8.386

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

0.701 0.527 0.942 0.515 0.273 0.539 0.583 0.076 0.364 0.850 0.227 0.706 0.745 0.957 0.041 0.134 0.044 0.156 0.598 0.778 0.244 0.788 0.791 0.671 0.759 0.580 0.535

7.009 5.267 9.416 5.145 2.732 5.385 5.831 0.757 3.643 8.498 2.268 7.055 7.453 9.569 0.412 1.337 0.442 1.559 5.978 7.777 2.441 7.882 7.912 6.714 7.588 5.801 5.355

Este gráfico no está disponible Si edita esta forma o guarda el diferente, difer ente, el gráfico gráfico n no o se podr podr

43 44 45 46 47 48 49 50

0.409 0.445 0.195 0.770 0.344 0.039 0.105 0.533

4.091 4.448 1.949 7.697 3.444 0.385 1.054 5.326

51 52 53 54 55 56 57 58 59 60 61 62 63

0.188 0.055 0.220 0.452 0.511 0.763 0.710 0.320 0.368 0.274 0.232 0.759 0.371

1.882 0.551 2.202 4.516 5.106 7.628 7.104 3.201 3.684 2.742 2.319 7.587 3.708

64 65 66 67 68 69 70 71 72 73 74 75 76

0.193 0.743 0.016 0.250 0.117 0.411 0.108 0.356 0.789 0.679 0.009 0.476 0.667

1.929 7.427 0.161 2.504 1.166 4.109 1.077 3.565 7.886 6.790 0.094 4.759 6.667

77 78 79 80 81 82 83 84 85 86 87 88 89

0.622 0.238 0.705 0.595 0.839 0.346 0.511 0.905 0.868 0.681 0.752 0.419 0.579

6.216 2.378 7.048 5.950 8.386 3.463 5.113 9.055 8.676 6.813 7.519 4.185 5.789

90 91 92

0.406 0.692 0.905

4.057 6.925 9.049

93 94 95 96 97 98 99 100

0.472 0.575 0.836 0.887 0.705 0.175 0.988 0.928

4.717 5.751 8.357 8.872 7.050 1.747 9.875 9.277

en su versión de Excel.

libro en un formato de archivo á utilizar.

Comprobar aleatoriedad de los datos CORRIDA DE LA MEDIA

#

MUESTRA 3

S

N° corridas

Media

1 2 3 4 5 6 7 8

24 44 10 5 8 4 26 62

0 1 0 0 0 0 1 1

1 1 1 0 0 0 1 0

24.17

9 10 11 12 13 14 15 16 17 18

2 4 18 1 29 22 4 12 54 10

0 0 0 0 1 0 0 0 1 0

1 0 0 0 1 1 0 0 1 1

19 20 21 22 23 24 25 26 27 28 29

22 6 62 13 2 17 2 31 3 8 29

0 0 1 0 0 0 0 1 0 0 1

0 0 1 1 0 0 0 1 1 0 1

30 31 32 33 34 35 36 37 38 39 40 41 42

18 12 9 41 2 16 23 26 70 8 2 114 77

0 0 0 1 0 0 0 1 1 0 0 1 1

1 0 0 1 1 0 0 1 0 1 0 1 0

43 44 45

7 19 9

0 0 0

1 0 0

Co N alfa n1 n2 Valor esperado Varianza Estadisco Valor en tabla

Conclusión

46 47 48 49 50 51 52 53

4 1 45 1 19 1 13 1

0 0 1 0 0 0 0 0

0 0 1 1 0 0 0 0

54 55 56 57 58 59 60 61 62 63 64 65 66

14 17 3 8 13 12 6 36 2 6 25 33 23

0 0 0 0 0 0 0 1 0 0 1 1 0

0 0 0 0 0 0 0 1 1 0 1 0 1

67 68 69 70 71 72 73 74 75 76 77 78 79

30 4 28 2 16 12 33 5 41 106 8 1 15

1 0 1 0 0 0 1 0 1 1 0 0 0

1 1 1 1 0 0 1 1 1 0 1 0 0

80 81 82 83 84 85 86 87 88 89 90 91 92

66 20 13 12 44 72 5 14 13 7 38 29 18

1 0 0 0 1 1 0 0 0 0 1 1 0

1 1 0 0 1 0 1 0 0 0 1 0 1

93 94 95

27 87 19

1 1 0

1 0 1

96 97 98 99 100 101 102 103

60 19 10 37 2 58 9 2

1 0 0 1 0 1 0 0

1 1 0 1 1 1 1 0

104 105 106 107 108 109 110 111 112 113 114 115 116

3 27 1 51 25 33 61 10 13 15 5 31 26

0 1 0 1 1 1 1 0 0 0 0 1 1

0 1 1 1 0 0 0 1 0 0 0 1 0

117 118 119 120 121 122 123 124 125 126 127 128 129

0 9 19 7 61 11 1 16 69 58 16 45 18

0 0 0 0 1 0 0 0 1 1 0 1 0

1 0 0 0 1 1 0 0 1 0 1 1 1

130 131 132 133 134 135 136 137 138 139 140 141 142

13 23 32 2 48 3 18 16 13 20 82 5 10

0 0 1 0 1 0 0 0 0 0 1 0 0

0 0 1 1 1 1 0 0 0 0 1 1 0

143 144 145

62 92 42

1 1 1

1 0 0

146 147 148 149 150

83 104 38 2 35

1 1 1 0 1

0 0 0 1 1

Encont Enc ontrar rar lla a distri distribic bición ión d de e pro probab babil ilii

70 150 0.05 97 53 69.547 31.074 14.433

MUESTRA 3

1.960

1 1 2 2 2 2 2 2 2 2

No se acepta la hipotesis nula. Los datos no son independientes, por lo tanto la secuencia NO es aleatoria.

0 1 1 1 1 1 1

Promedio Min Max Rango n # intervalos Tamaño

1 2 3 4 5 6 7 8

2 2 2 3 3 3 3 4 4 4 4 4 5 5 5 5 5 6 6 6 7 7 7 8 8 8 8

80

72

70 60 50 40 30 20 10 0

15

Con la ay

Ho= Los valore H1= Los valore Landa N Chi-Tabla

8 9 9 9 9 10 10 10 10 10 11 12 12 12 12 12 13 13 13 13 13 13 13 13 14 14 15 15 16 16 16 16 16 17 17 18 18 18 18 18 19 19 19 19 19 20 20 22 22 23

Clase 15 30 45 60 75 90 105

120

El chichi-cal calcul cula a

23 23 24 25 25 26 26 26 27 27 28 29 29 29 30 31 31 32 33 33 33 35 36 37 38 38 41 41 42 44 44 45 45 48 51 54 58 58 60 61 61 62 62 62 66 69 70 72 77 82

83 87 92 104 106 114

ad de los datos

Generar 1

24.17 0.00 114.00 115.00 150.00 8.18 15.000 Intervalos 0 15 30 45 60 75

15 30 45 60 75 90

0 19 05

1 10 25 0

Clase

Frecuencia 15 30 45 60 75 90

72 37 18 6 9 4

1 10 25 0

2 2

y mayor...

0

Hist ograma og rama Muest ra 3

37 18

9

6 30

45

60

75

4

2

2

90

105

120

da visual se puede notar que el histograma se comporta como una distribución exponenial negava.

se ajustan a una distribución exponencial negava no se ajustan a una distribución exponencial negava 0.04136789851 150 12.5916

Frecu Fre cuen enci cia a Fo 72 37 18 6 9 4 2 2

Prob Probab abil ilid idad ad PI EXP EXP

Fe Fe=P =PI* I*N N

(( ((Fo Fo-- Fe Fe)^ )^2) 2)/Fe /Fe

46.2 46.233 33% % 24.8 24.858 58% % 13.3 13.365 65% % 7.18 .186% 3.86 3.864% 4% 2.07 .077% 1.11 1.117% 7%

69.3 69.350 5016 1603 034 4 37.2 37.287 8719 1954 541 1 20.0 20.048 4804 0422 221 1 10.7 0.7791 914 426 5.79 5.7955 5574 7414 147 7 3.1 3.116 160 080 808 838 1.67 1.6754 5409 0946 466 6

1.29 1.299% 9%

1.94 1.9483 8394 9498 988 8 0.00 0.0013 1366 6680 8056 565 5

0.10 0.1012 1249 4922 2281 816 6 0.00 0.0022 2212 1205 0517 172 2 0.20 0.2092 9221 2127 2717 178 8 2.11 118 892 925 585 856 674 1.77 1.7717 1756 5630 3066 663 3 0.250 507 735 358 820 203 3 0.06 0.0628 2885 8553 5313 139 9

Chi-cuadrad Chi-c uadrado o 4.51835287237 4.51835287237

o es menor al chi-tabla, se acepta la hipotesis nula, es decir que los valores se ajustan a una distribución exponencial.

0 numeros aleatorios con distribución exponencial Landa

#

0.25

Al Alea eat. t. Unif Unifor orme me Alea Aleato to.. Expo Expone nenc ncia ial l 1 0.76 0.761902 19028943 89432 2 5.74030 5.740306725 67258616 86166 6 2 0.206194235388 0.923665906456564 3 0.19 0.196086 60863156 31565 5 0.87305349 0.87305349336 3360674 0674 4 0.75 0.757819 78191502 150251 51 5.6 5.67228 72282075 20756419 64196 6 5 6 7 8 9 10 11 12 13 14 15

0.138213333031 0.594990100251027 0.089677918805 0.375827226850215 0.3314905062 0.331490 506299 99 1.6 1.61081 10818724 87241725 17252 2 0.58 0.587991 79911316 13162 2 3.54684 3.546841618 16186805 68056 6 0.7002268127 0.700226 812752 52 4.8 4.81891 18916531 65311098 10985 5 0.3131355495 0.313135 549514 14 1.5 1.50247 02473250 32506063 60637 7 0.3288515752 0.328851 575207 07 1.5 1.59505 95059868 98683140 31405 5 0.8683134969 0.868313 496991 91 8.1 8.10932 09324633 46333332 33324 4 0.1505963210 0.150596 321035 35 0.6 0.65288 52882919 29194449 44495 5 0.097285352062 0.409395120011817 0.2779758183 0.277975 818309 09 1.3 1.30278 02786592 65920142 01424 4

16 17 18 19 20 21 22 23 24 25 26 27 28

0.694964 0.69 49646821 682186 86 4.7 4.74931 49310851 08518726 87268 8 0.903946 0.9039468083 80836 6 9.37141 9.371412645 26454860 48607 7 0.324238 0.3242382301 23011 1 1.56765 1.567658705 87058260 82609 9 0.450347 0.4503479010 901001 01 2.393878 2.3938789926 9926937 937 0.169539760622 0.743100906391594 0.5355008944 0.535500 894466 66 3.0 3.06718 67182585 25855362 53625 5 0.9952518078 0.995251 807827 27 21. 21.3999 39996531 65314429 44292 2 0.5217862750 0.521786 275009 09 2.9 2.95079 50790092 00920337 03373 3 0.117705301042 0.500916611918789 0.6378909104 0.637890 910473 73 4.0 4.06323 63239041 90410811 08111 1 0.5801610799 0.580161 079953 53 3.4 3.47153 71536659 66598618 86186 6 0.477926 0.4779269992 999243 43 2.599791 2.5997914107 4107322 322 0.4295165095 0.429516 509543 43 2.2 2.24508 45084195 41952996 29968 8

29 0.110841488556 0.469919025104671 30 0.658918 0.6589183991 399154 54 4.3 4.30253 02534126 41266349 63491 1 31 0.540861 0.5408610902 090246 46 3.1 3.11360 13609916 99163096 30966 6

Este gráfico no está disp isponible en su v Si edita esta forma o guarda el libro en gráfico no se podrá utilizar.

32 33 34 35 36 37 38 39

0.155888124837 0.677880958638327 0.9823751586 0.982375 158692 92 16. 16.1537 15378373 83736520 65201 1 0.8384035542 0.838403 554214 14 7.2 7.29061 90612508 25081530 15309 9 0.6685516248 0.668551 624891 91 4.4 4.41713 17132850 28507077 70779 9 0.9784602565 0.978460 256586 86 15. 15.3514 35142207 22077499 74992 2 0.686161 0.6861610696 069651 51 4.635501 4.6355015414 5414224 224 0.163037 0.1630375121 51212 2 0.711904107 0.7119041073766 376698 98 0.4906423955 0.490642 395561 61 2.6 2.69841 98419785 97854588 45885 5

40 41 42 43 44 45 46 47 48 49 50 51 52

0.163327938184 0.281225 0.2812251863 186318 18 0.4386778231 0.438677 823199 99 0.161444 0.1614443456 34562 2 0.196713 0.1967136777 67771 1 0.6452271709 0.645227 170916 16 0.4834558461 0.483455 846173 73 0.5201419666 0.520141 966608 08 0.061803775724 0.3494555023 0.349455 502382 82 0.9091684511 0.909168 451113 13 0.5347604139 0.534760 413958 58 0.6521636985 0.652163 698597 97

53 54 55 56 57 58 59 60 61 62 63 64 65

0.272240 0.27 22408330 833015 15 1.2 1.27114 71140400 04003903 39034 4 0.979675 0.9796757740 77406 6 15.5837 15.58376683 66833605 36055 5 0.121969409378 0.520295378797181 0.008005166977 0.032149521429151 0.4989442747 0.498944 274736 36 2.7 2.76415 64151824 18240406 04066 6 0.6858032585 0.685803 258586 86 4.6 4.63094 30943697 36970805 08053 3 0.8961614654 0.896161 465411 11 9.0 9.05967 59672553 25533026 30268 8 0.5297811266 0.529781 126623 23 3.0 3.01822 18228018 80185668 56682 2 0.6371018030 0.637101 803072 72 4.0 4.05453 54531733 17331418 14187 7 0.7266937001 0.726693 700171 71 5.1 5.18864 88648541 85413887 38876 6 0.9155168383 0.915516 838329 29 9.8 9.88481 84812138 21385853 58539 9 0.8056603109 0.805660 310955 55 6.5 6.55259 52590706 07065091 50919 9 0.4144668956 0.414466 895627 27 2.1 2.14093 40930228 02287864 78648 8

66 67 68 69 70 71 72 73 74 75 76 77 78

0.121201004572 0.516796326361297 0.8225451711 0.822545 171151 51 6.9 6.91615 16156751 67512564 25647 7 0.5128002353 0.512800 235332 32 2.8 2.87632 76324182 41824672 46726 6 0.3697929985 0.369792 998573 73 1.8 1.84682 46827759 77594848 48487 7 0.377015 0.3770158440 84406 6 1.89293 1.892936769 67695840 58406 6 0.425984 0.4259848800 88006 6 2.22039 2.220398166 81666020 60206 6 0.8256001636 0.825600 163622 22 6.9 6.98561 85618822 88228374 83742 2 0.5926701274 0.592670 127426 26 3.5 3.59252 92527696 76963645 36451 1 0.113888674536 0.483650747050134 0.6916355097 0.691635 509787 87 4.7 4.70589 05891143 11436174 61745 5 0.3525924084 0.352592 408469 69 1.7 1.73911 39116845 68455000 50007 7 0.863479 0.8634799750 975011 11 7.965135 7.9651358876 8876127 127 0.5969648182 0.596964 818292 92 3.6 3.63492 34925685 56852899 28993 3

0.713292348635973 1.320828 1.3208286563 6563334 334 2.3 2.30984 09840992 09924089 40898 8 0.704297304 0.7042973047289 728967 67 0.876176251 0.8761762513950 395041 41 4.1 4.14511 45110449 04496592 65928 8 2.6 2.64237 42378029 80299199 91993 3 2.9 2.93705 37059930 99303775 37757 7 0.255184630118388 1.7 1.71978 19782312 23124557 45577 7 9.5 9.59499 94994396 43960833 08334 4 3.0 3.06081 60811069 10691357 13574 4 4.2 4.22409 24093232 32325884 58844 4

79 0.220417 0.2204177143 71432 2 0.995988135 0.9959881357049 704908 08 80 0.39 0.390323 03232952 295249 49 1.9 1.97930 79305818 58180857 08572 2 81 0.164858351833 0.720615719979128

82 83 84 85 86 87 88 89

0.447277 0.44 72779671 967193 93 0.5594113711 0.559411 371131 31 0.0935821053 0.093582 105311 11 0.4839810376 0.483981 037671 71 0.3185658435 0.318565 843557 57 0.9241281670 0.924128 167036 36 0.8250462908 0.825046 290829 29 0.8215780750 0.821578 075071 71

2.3 2.37160 71600227 02279352 93527 7 3.2 3.27857 78574612 46129306 93068 8 0.3 0.39301 93019307 93074708 47085 5 2.6 2.64644 46447061 70619067 90679 9 1.5 1.53422 34222592 25926025 60259 9 10. 10.3148 31483908 39082609 26095 5 6.9 6.97293 72935436 54362934 29344 4 6.8 6.89441 94416675 66752117 21171 1

90 91 92 93 94 95 96 97 98 99 100

0.437538 0.43 75381941 194112 12 0.668 0.668080 080454 4547 7 0.646418 0.6464180379 037912 12 0.5435331932 0.543533 193238 38 0.550414 0.5504145085 508585 85 0.8322873739 0.832287 373931 31 0.5684296651 0.568429 665164 64 0.9050557180 0.905055 718095 95 0.7831143135 0.783114 313527 27 0.3118005042 0.311800 504232 32 0.871076706 0.87107 6706798 798

2.3 2.30172 01728191 81914085 40856 6 4.411 4.411450 450691 691466 46658 58 4.158559 4.1585598468 8468602 602 3.1 3.13695 36957176 71761989 19898 8 3.197717 3.1977170036 0036291 291 7.1 7.14201 42013293 32934684 46846 6 3.3 3.36129 61299123 91238534 85346 6 9.4 9.41786 17860262 02628287 82876 6 6.1 6.11353 13539418 94187682 76826 6 1.4 1.49470 94706073 60732074 20743 3 8.1 8.19415 94150711 07113003 30039 9

rsión de Excel. un formato de archivo diferente, el

Actividad-5 - Generación Manual de Variables Aleatorias

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