Actividad 5 - Generación Manual de Variables Aleatorias

September 30, 2022 | Author: Anonymous | Category: N/A

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ACTIVIDAD 5 GENERACIÓN MANUAL DE VARIABLES ALEATORIAS

ANGIE PAOLA MUÑOZ ID: 100070675 WILLIAM ADOLFO PUPO ID: 100066863

INGENIERIA INDUSTRIAL MODELAMIENTO Y SIMULACION 2022

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.

MUESTRA 1 PRUEBA DE CORRIDAS NUMEROS ALEATORIOS

S

# DE CORRIDAS

1 1 1 1 1 1 1

1 0 0 0 0 0 0

1 1 1 1

0 0 0 0

MEDIA

1 2 3 4 5 6 7

0 1 1 1 1 1 1

24.18

8

1

9 10 11

1 2 2

12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

2 2 2 2 2 2 2 2 2 3 3 3 3 4 4 4 4 4 5 5 5 5 5

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

35 36 37

6 6 6

1 1 1

0 0 0

Co n ALFA n1 n2 VALOR ESPERADO VARIANZA ESTADISTICO

2 150 0.05 53 97 69.55 31.07 12.11719

VALOR EN TABLAS 1.95996

38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56

7 7 7 8 8 8 8 8 9 9 9 9 10 10 10 10 10 11 12

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

57 58 59 60 61 62 63 64 65 66 67 68

12 12 12 12 13 13 13 13 13 13 13 13

1 1 1 1 1 1 1 1 1 1 1 1

0 0 0 0 0 0 0 0 0 0 0 0

69 70 71 72 73 74 75 76 77 78 79 80 81 82

14 14 15 15 16 16 16 16 16 17 17 18 18 18

1 1 1 1 1 1 1 1 1 1 1 1 1 1

0 0 0 0 0 0 0 0 0 0 0 0 0 0

83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101

18 18 19 19 19 19 19 20 20 22 22 23 23 23 24 25 25 26 26

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

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

102 103 104 105 106 107 108 109 110 111 112 113

26 27 27 28 29 29 29 30 31 31 32 33

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

114 115 116 117 118 119 120 121 122 123 124 125 126 127

33 33 35 36 37 38 38 41 41 42 44 44 45 45

0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146

48 51 54 58 58 60 61 61 62 62 63 66 69 70 72 77 82 83 87

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

147 148 149 150

92 104 106 114

0 0 0 0

0 0 0 0

CONCLUSION

LOS DATOS NO SON INDEPENDIENTES

Nivel de signifcancia:

0.05

SUMA DE (X-VALOR MEDIO)2

1213.2600

X-VALOR MEDIO

(X-VALOR MEDIO)2

5.54 2.85 1 10 9 150 8

-4.5400 -4.5400 -4.5400 -4.5400 -4.5400 -4.5400 -4.5400

20.6116 20 20.6116 20.6116 20.6116 20.6116 20.6116 20.6116

-4.5400

20.6116

1.1001 831 0.04718

-4.5400 -4.5400 -4.5400

20.6116 20.6116 20.6116

0.9504

-4.5400 -4.5400 -3.5400 -3.5400 -3.5400 -3.5400 -3.5400 -3.5400 -3.5400 -3.5400 -3.5400 -3.5400 -3.5400 -3.5400 -3.5400 -3.5400 -3.5400 -2.5400 -2.5400 -2.5400 -2.5400 -2.5400 -2.5400

20.6116 20.6116 12.5316 12.5316 12.5316 12.5316 12.5316 12.5316 12.5316 12.5316 12.5316 12.5316 12.5316 12.5316 12.5316 12.5316 12.5316 6.4516 6.4516 6.4516 6.4516 6.4516 6.4516

--2 2..5 54 40 00 0 -2.5400

6 6..4 45 51 16 6 6.4516

MEDIA DESVIACION MINIMO MAXIMO RANGO n # INTERVALOS

INTERVALOS RAIZ de n 12.2474 TAMAÑO INTERVALO N K-S D+

-2.5400 -2.5400 -2.5400 -2.5400 -2.5400 -2.5400 -2.5400 -1.5400 -1.5400 -1.5400 -1.5400 -1.5400 -1.5400 -1.5400 -1.5400 -1.5400 -1.5400 -1.5400 -1.5400

6.4516 6.4516 6.4516 6.4516 6.4516 6.4516 6.4516 2.3716 2.3716 2.3716 2.3716 2.3716 2.3716 2.3716 2.3716 2.3716 2.3716 2.3716 2.3716

-1.5400 -1.5400 -1.5400 -1.5400 -0.5400 -0.5400 -0.5400 -0.5400 -0.5400 -0.5400 -0.5400 -0.5400

2.3716 2.3716 2.3716 2.3716 0.2916 0.2916 0.2916 0.2916 0.2916 0.2916 0.2916 0.2916

-0.5400 -0.5400 -0.5400 -0.5400 -0.5400 -0.5400 -0.5400 -0.5400 -0.5400 0.4600 0.4600 0.4600 0.4600 0.4600

0.2916 0.2916 0.2916 0.2916 0.2916 0.2916 0.2916 0.2916 0.2916 0.2116 0.2116 0.2116 0.2116 0.2116

0.4600 0.4600 0.4600 0.4600 0.4600 0.4600 0.4600 1.4600 1.4600 1.4600 1.4600 1.4600 1.4600 1.4600 1.4600 1.4600 1.4600 1.4600 1.4600

0.2116 0.2116 0.2116 0.2116 0.2116 0.2116 0.2116 2.1316 2.1316 2.1316 2.1316 2.1316 2.1316 2.1316 2.1316 2.1316 2.1316 2.1316 2.1316

1.4600 2.4600 2.4600 2.4600 2.4600 2.4600 2.4600 2.4600 2.4600 2.4600 2.4600 2.4600

2.1316 6.0516 6.0516 6.0516 6.0516 6.0516 6.0516 6.0516 6.0516 6.0516 6.0516 6.0516

2.4600 2.4600 2.4600 2.4600 2.4600 2.4600 2.4600 2.4600 3.4600 3.4600 3.4600 3.4600 3.4600 3.4600

6.0516 6.0516 6.0516 6.0516 6.0516 6.0516 6.0516 6.0516 11.9716 11.9716 11.9716 11.9716 11.9716 11.9716

3.4600 3.4600 3.4600 3.4600 3.4600 3.4600 3.4600 3.4600 4.4600 4.4600 4.4600 4.4600 4.4600 4.4600 4.4600 4.4600 4.4600 4.4600 4.4600

11.9716 11.9716 11.9716 11.9716 11.9716 11.9716 11.9716 11.9716 19.8916 19.8916 19.8916 19.8916 19.8916 19.8916 19.8916 19.8916 19.8916 19.8916 19.8916

4.4600 4.4600 4.4600 4.4600

19.8916 19.8916 19.8916 19.8916

D+ K-S

0.9504 0.04718

PRUEBA KOLMOGOROV -SMIRNOV X

XI

Fo(X/N)

FoAcum

F(x) Acum o Acum-F(x) Acu

CONCLUSION

XI

1 2 3 4 5 6 7

1 1 1 1 1 1 1

0.0012 0.0012 0.0012 0.0012 0.0012 0.0012 0.0012

0.0012 0.0024 0.0036 0.0048 0.0060 0.0072 0.0084

0.1813 0.3297 0.4512 0.5507 0.6321 0.6988 0.7534

0.1801 0.3273 0.4476 0.5459 0.6261 0.6916 0.7450

8

1 1 1 1

0.0012

0.0096

0.7981

0.7885

8

9 10 11

0.0012 0.0012 0.0012

0.0108 0.0120 0.0132

0.8347 0.8647 0.8892

0.8239 0.8526 0.8760

9 10 11

12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3

0.0012 0.0012 0.0024 0.0024 0.0024 0.0024 0.0024 0.0024 0.0024 0.0024 0.0024 0.0024 0.0024 0.0024 0.0024 0.0024 0.0024 0.0036 0.0036 0.0036 0.0036 0.0036 0.0036

0.0144 0.0156 0.0181 0.0205 0.0229 0.0253 0.0277 0.0301 0.0325 0.0349 0.0373 0.0397 0.0421 0.0445 0.0469 0.0493 0.0517 0.0554 0.0590 0.0626 0.0662 0.0698 0.0734

0.9093 0.9257 0.9392 0.9502 0.9592 0.9666 0.9727 0.9776 0.9817 0.9850 0.9877 0.9899 0.9918 0.9933 0.9945 0.9955 0.9963 0.9970 0.9975 0.9980 0.9983 0.9986 0.9989

0.8948 0.9101 0.9211 0.9298 0.9364 0.9414 0.9450 0.9475 0.9492 0.9501 0.9504 0.9502 0.9497 0.9487 0.9476 0.9461 0.9446 0.9416 0.9386 0.9354 0.9322 0.9288 0.9255

12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

35 36 37

3 3 3

0.0036 0.0036 0.0036

0.0770 0.0806 0.0842

0.9991 0.9993 0.9994

0.9221 0.9186 0.9152

35 36 37

NO SE AJUSTA A UNA DISTRIBUCION EXPONENCIAL

1 2 3 4 5 6 7

38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56

3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4

0.0036 0.0036 0.0036 0.0036 0.0036 0.0036 0.0036 0.0048 0.0048 0.0048 0.0048 0.0048 0.0048 0.0048 0.0048 0.0048 0.0048 0.0048 0.0048

0.0878 0.0915 0.0951 0.0987 0.1023 0.1059 0.1095 0.1143 0.1191 0.1239 0.1288 0.1336 0.1384 0.1432 0.1480 0.1528 0.1576 0.1625 0.1673

0.9995 0.9996 0.9997 0.9997 0.9998 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.9117 0.9081 0.9046 0.9010 0.8975 0.8939 0.8903 0.8856 0.8808 0.8760 0.8712 0.8664 0.8616 0.8568 0.8520 0.8471 0.8423 0.8375 0.8327

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

4 4 4 4 5 5 5 5 5 5 5 5

0.0048 0.0048 0.0048 0.0048 0.0060 0.0060 0.0060 0.0060 0.0060 0.0060 0.0060 0.0060

0.1721 0.1769 0.1817 0.1865 0.1925 0.1986 0.2046 0.2106 0.2166 0.2226 0.2286 0.2347

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.8279 0.8231 0.8183 0.8135 0.8075 0.8014 0.7954 0.7894 0.7834 0.7774 0.7714 0.7653

57 58 59 60 61 62 63 64 65 66 67 68

69 70 71 72 73 74 75 76 77 78 79 80 81 82

5 5 5 5 5 5 5 5 5 6 6 6 6 6

0.0060 0.0060 0.0060 0.0060 0.0060 0.0060 0.0060 0.0060 0.0060 0.0072 0.0072 0.0072 0.0072 0.0072

0.2407 0.2467 0.2527 0.2587 0.2647 0.2708 0.2768 0.2828 0.2888 0.2960 0.3032 0.3105 0.3177 0.3249

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.7593 0.7533 0.7473 0.7413 0.7353 0.7292 0.7232 0.7172 0.7112 0.7040 0.6968 0.6895 0.6823 0.6751

69 70 71 72 73 74 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

6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7

0.0072 0.0072 0.0072 0.0072 0.0072 0.0072 0.0072 0.0084 0.0084 0.0084 0.0084 0.0084 0.0084 0.0084 0.0084 0.0084 0.0084 0.0084 0.0084

0.3321 0.3394 0.3466 0.3538 0.3610 0.3682 0.3755 0.3839 0.3923 0.4007 0.4091 0.4176 0.4260 0.4344 0.4428 0.4513 0.4597 0.4681 0.4765

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.6679 0.6606 0.6534 0.6462 0.6390 0.6318 0.6245 0.6161 0.6077 0.5993 0.5909 0.5824 0.5740 0.5656 0.5572 0.5487 0.5403 0.5319 0.5235

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

7 8 8 8 8 8 8 8 8 8 8 8

0.0084 0.0096 0.0096 0.0096 0.0096 0.0096 0.0096 0.0096 0.0096 0.0096 0.0096 0.0096

0.4850 0.4946 0.5042 0.5138 0.5235 0.5331 0.5427 0.5523 0.5620 0.5716 0.5812 0.5909

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.5150 0.5054 0.4958 0.4862 0.4765 0.4669 0.4573 0.4477 0.4380 0.4284 0.4188 0.4091

102 103 104 105 106 107 108 109 110 111 112 113

114 115 116 117 118 119 120 121 122 123 124 125 126 127

8 8 8 8 8 8 8 8 9 9 9 9 9 9

0.0096 0.0096 0.0096 0.0096 0.0096 0.0096 0.0096 0.0096 0.0108 0.0108 0.0108 0.0108 0.0108 0.0108

0.6005 0.6101 0.6197 0.6294 0.6390 0.6486 0.6582 0.6679 0.6787 0.6895 0.7004 0.7112 0.7220 0.7329

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.3995 0.3899 0.3803 0.3706 0.3610 0.3514 0.3418 0.3321 0.3213 0.3105 0.2996 0.2888 0.2780 0.2671

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

9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10

0.0108 0.0108 0.0108 0.0108 0.0108 0.0108 0.0108 0.0108 0.0120 0.0120 0.0120 0.0120 0.0120 0.0120 0.0120 0.0120 0.0120 0.0120 0.0120

0.7437 0.7545 0.7653 0.7762 0.7870 0.7978 0.8087 0.8195 0.8315 0.8436 0.8556 0.8676 0.8797 0.8917 0.9037 0.9158 0.9278 0.9398 0.9519

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.2563 0.2455 0.2347 0.2238 0.2130 0.2022 0.1913 0.1805 0.1685 0.1564 0.1444 0.1324 0.1203 0.1083 0.0963 0.0842 0.0722 0.0602 0.0481

128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146

147 148 149 150

10 10 10 10 831

0.0120 0.0120 0.0120 0.0120

0.9639 0.9759 0.9880 1.0000

1.0000 1.0000 1.0000 1.0000

0.0361 0.0241 0.0120 0.0000

147 148 149 150

150

150

CHI CALCULADO CHI TABLA

35117293836173 177.389749986549 PRUEBA CHI CUADRADO

X

Fo

FoAcum

F(x)

DATOS SEGUN EXPONENCIAL (Ei)

(X-Ei)^2/Ei

1 1 1 1 1 1 1

0..0909 0 0.0909 0. 0.0909 0.0909 0.0909 0.0909 0.0909

0.0909 0.1818 0.2727 0.3636 0.4545 0.5455 0.6364

0.1637 0.1341 0.1098 0.0899 0.0736 0.0602 0.0493

136.0731 111.4072 91.2125 74.6785 61.1416 50.0585 40.9844

134 109 89 73 59 48 39

1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3

0.0909

0.7273

0.0404

33.5552

32

0.0909 0.0909 0.0909

0.8182 0.9091 1.0000

0.0331 0.0271 0.0222

27.4727 22.4927 18.4155

26 21 16

0.0909 0.0909 0.1818 0.1818 0.1818 0.1818 0.1818 0.1818 0.1818 0.1818 0.1818 0.1818 0.1818 0.1818 0.1818 0.1818 0.1818 0.2727 0.2727 0.2727 0.2727 0.2727 0.2727

1.0909 1.1818 1.3636 1.5455 1.7273 1.9091 2.0909 2.2727 2.4545 2.6364 2.8182 3.0000 3.1818 3.3636 3.5455 3.7273 3.9091 4.1818 4.4545 4.7273 5.0000 5.2727 5.5455

0.0181 0.0149 0.0122 0.0100 0.0082 0.0067 0.0055 0.0045 0.0037 0.0030 0.0025 0.0020 0.0016 0.0013 0.0011 0.0009 0.0007 0.0006 0.0005 0.0004 0.0003 0.0003 0.0002

15.0773 12.3443 10.1066 8.2746 6.7747 5.5466 4.5412 3.7180 3.0441 2.4923 2.0405 1.6706 1.3678 1.1198 0.9169 0.7507 0.6146 0.5032 0.4120 0.3373 0.2762 0.2261 0.1851

13 10 7 5 3 2 1 1 0 0 0 0 0 1 1 2 3 12 16 21 27 34 43

3 3 3

0.2727 0.2727 0.2727

5.8182 6.0909 6.3636

0.0002 0.0001 0.0001

0.1516 0.1241 0.1016

54 67 83

CONCLUSION

NO SE AJUSTA A UNA DISTRIBUCION EXPONENCIAL

4 4 4 4 4 4 4 4 4 4 4 4

0.2727 0.2727 0.2727 0.2727 0.2727 0.2727 0.2727 0.3636 0.3636 0.3636 0.3636 0.3636 0.3636 0.3636 0.3636 0.3636 0.3636 0.3636 0.3636

6.6364 6.9091 7.1818 7.4545 7.7273 8.0000 8.2727 8.6364 9.0000 9.3636 9.7273 10.0909 10.4545 10.8182 11.1818 11.5455 11.9091 12.2727 12.6364

0.0001 0.0001 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0832 0.0681 0.0558 0.0456 0.0374 0.0306 0.0251 0.0205 0.0168 0.0137 0.0113 0.0092 0.0075 0.0062 0.0051 0.0041 0.0034 0.0028 0.0023

102 126 155 191 235 288 353 772 945 1156 1413 1728 2112 2582 3155 3856 4711 5756 7032

4 4 4 4 5 5 5 5 5 5 5 5

0.3636 0.3636 0.3636 0.3636 0.4545 0.4545 0.4545 0.4545 0.4545 0.4545 0.4545 0.4545 0.

13.0000 13.3636 13.7273 14.0909 14.5455 15.0000 15.4545 15.9091 16.3636 16.8182 17.2727 17.7273

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0019 0.0015 0.0012 0.0010 0.0008 0.0007 0.0006 0.0005 0.0004 0.0003 0.0003 0.0002

8591 10495 12820 15660 29892 36513 44599 54475 66538 81272 99268 121249

5 5 5 5 5 5 5 5 5 6 6 6 6 6

0. 0.4545 0.4545 0. 0.4545 0. 0.4545 0. 0.4545 0. 0.4545 0. 0.4545 0. 0.4545 0. 0.4545 0. 0.5455 0. 0.5455 0. 0.5455 0. 0.5455 0. 0.5455 0.

18.1818 18.6364 19.0909 19.5455 20.0000 20.4545 20.9091 21.3636 21.8182 22.3636 22.9091 23.4545 24.0000 24.5455

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0002 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

148096 180887 220938 269857 329606 402584 491719 600590 733564 1290213 1575872 1924777 2350931 2871436

3 3 3 3 3 3 3

7 7 7 7 7 7 7 7 7 7 7 7

0..5455 0 0.5455 0. 0.5455 0. 0.5455 0. 0.5455 0. 0.5455 0. 0.5455 0. 0.6364 0. 0.6364 0. 0.6364 0. 0.6364 0. 0.6364 0. 0.6364 0. 0.6364 0. 0.6364 0. 0.6364 0. 0.6364 0. 0.6364 0. 0.6364 0.

25.0909 25.6364 26.1818 26.7273 27.2727 27.8182 28.3636 29.0000 29.6364 30.2727 30.9091 31.5455 32.1818 32.8182 33.4545 34.0909 34.7273 35.3636 36.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

3507183 4283685 5232108 6390513 7805393 9533532 11644285 19358220 23644186 28879078 35272988 43082528 52621122 64271586 78501496 95881947 117110477 143039063 174708309

7 8 8 8 8 8 8 8 8 8 8 8

0. 0.6364 0.7273 0. 0.7273 0. 0.7273 0. 0.7273 0. 0.7273 0. 0.7273 0. 0.7273 0.7273 0.7273 0.7273 0.7273

36.6364 37.3636 38.0909 38.8182 39.5455 40.2727 41.0000 41.7273 42.4545 43.1818 43.9091 44.6364

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

213389214 340420152 415790116 507847198 620285972 757619001 925357941 1130234745 1380471838 1686112114 2059421990 2515383703

8 8 8 8 8 8 8 8 9 9 9 9 9 9

0.7273 0.7273 0.7273 0.7273 0.7273 0.7273 0.7273 0.7273 0.8182 0.8182 0.8182 0.8182 0.8182 0.8182

45.3636 46.0909 46.8182 47.5455 48.2727 49.0000 49.7273 50.4545 51.2727 52.0909 52.9091 53.7273 54.5455 55.3636

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

3072296596 3752511540 4583327948 5598089401 6837521838 8351368036 ### ### ### ### ### ### ### ###

6 6 6 6 6 6 6

9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 831

0.8182 0.8182 0.8182 0.8182 0.8182 0.8182 0.8182 0.8182 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091

56.1818 57.0000 57.8182 58.6364 59.4545 60.2727 61.0909 61.9091 62.8182 63.7273 64.6364 65.5455 66.4545 67.3636 68.2727 69.1818 70.0909 71.0000 71.9091

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ###

0.9091 0.9091 0.9091 0.9091

72.8182 73.7273 74.6364 75.5455

0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000

### ### ### ###

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MUESTRA 2

NUMEROS ALEATORIOS

t = t = t = t = t = t = t = t = t = t = t = t = t = t = t = t = t = tt = = t = t = t = t = t = t = t = t = t = t =

MEDIA

5.54

S

# DE CORRIDAS

1

1

3

1

1

9

2

1

1

0

5

3

1

1

0

2

4

1

1

0

4

5

1

1

0

7

6

1

1

0

3

7

1

1

0

7

8

1

1

0

9

9 10

1

1

0

4

1

1

0

3

11

1

1

0

5

12

1

1

0

9

13

1

1

0

4

14

2

1

0

10

15

2

1

0

9

16

2

1

0

4

17

2

1

0

18

3 8

19

2 2

1 1

0 0

4

20

2

1

0

6

21

2

1

0

3

22

2

1

0

2

23

2

1

0

9

24

2

1

0

10

25

2

1

0

4

26

2

1

0

3

27

2

1

0

8

28

2

1

0

3

29

3

1

0

t = t = t = t = t = t =

10

30

3

1

0

1

31

3

1

0

4

32

3

1

0

8

33

3

1

0

4

34

3

1

0

9

35

3

1

0

t = t = t = t = t = t = t = t = t =

7

36

3

1

0

5

37

3

1

0

7

38

3

1

0

10

39

3

1

0

4

40

3

1

0

9

41

3

1

0

8

42

3

1

0

9

43

3

1

0

7

44

3

1

0

6 6

45 46

4 4

1 1

0 0

2

47

4

1

0

9

48

4

1

0

3

49

4

1

0

6

50

4

1

0

5

51

4

1

0

8

52

4

1

0

4

53

4

1

0

6

54

4

1

0

2

55

4

1

0

10

56

4

1

0

7

57

4

1

0

7

58

4

1

0

6

59

4

1

0

8

60

4

1

0

3

61

5

1

0

3

62

5

1

0

2

63

5

1

0

4

64 65

5

1

0

5

1

0

t = t = t = t = t = t = t = t = t = t = t = t = t = t = t = t = t = t = t = t = t =

8

t = t = t = t = t = t =

3

66

5

1

0

3

67

5

1

0

5

68

5

1

0

5

69

5

1

0

9

70

5

1

0

5

71

5

1

0

t = t = t = t = t = t = t = t = t =

8

72

5

1

0

1

73

5

1

0

5

74

5

1

0

5

75

5

1

0

2

76

5

1

0

4

77

5

1

0

4

78

6

0

1

5

79

6

0

0

7

80

6

0

0

t = t = t = t = t = t = t = t = t = t = t = t = t = t = t = t = t = t = t =

10 10

81 82

6 6

0 0

0 0

7

83

6

0

0

10

84

6

0

0

8

85

6

0

0

1

86

6

0

0

10

87

6

0

0

3

88

6

0

0

2

89

6

0

0

9

90

7

0

0

1

91

7

0

0

2

92

7

0

0

10

93

7

0

0

3

94

7

0

0

9

95

7

0

0

8

96

7

0

0

10

97

7

0

0

5

98

7

0

0

8

99

7

0

0

t = t =

5

100 101

7

0

0

7

0

0

7

t = t = t = t = t = t =

8

102

7

0

0

3

103

8

0

0

1

104

8

0

0

6

105

8

0

0

5

106

8

0

0

7

107

8

0

0

t = t = t = t = t = t = t = t = t =

4

108

8

0

0

5

109

8

0

0

5

110

8

0

0

1

111

8

0

0

6

112

8

0

0

7

113

8

0

0

1

114

8

0

0

8

115

8

0

0

2

116

8

0

0

t = t = t = t = t = t = t = t = t = t = t = t = t = t = t = t = t = t = t =

6 8

117 118

8 8

0 0

0 0

7

119

8

0

0

1

120

8

0

0

1

121

8

0

0

10

122

9

0

0

1

123

9

0

0

4

124

9

0

0

8

125

9

0

0

2

126

9

0

0

1

127

9

0

0

8

128

9

0

0

6

129

9

0

0

1

130

9

0

0

4

131

9

0

0

10

132

9

0

0

10

133

9

0

0

5

134

9

0

0

6

135

9

0

0

2

136 137

10

0

0

10

0

0

t = t =

3

t = t = t = t = t = t =

10

138

10

0

0

2

139

10

0

0

5

140

10

0

0

8

141

10

0

0

9

142

10

0

0

2

143

10

0

0

t = t = t = t = t = t = t =

1

144

10

0

0

2

145

10

0

0

6

146

10

0

0

9

147

10

0

0

2

148

10

0

0

8

149

10

0

0

8

150

10

0

0

PRUEBA DE CORRIDAS

Nivel de signifcancia: SUMA DE (X-VALOR MEDIO)2

Co n ALFA

2

CONCLUSION

150

0.05

MEDIA DESVIACION

LOS DATOS NO SON INDEPENDIENTES

MINIMO

n1

73

n2

77

RANGO

75.95

n

VALOR ESPERADO

MAXIMO

VARIANZA

37.20

# INTERVALOS

ESTADISTICO

12.12485

INTERVALOS RAIZ de n

VALOR EN TABLAS 1.95996

TAMAÑO INTERVALO N K-S D+

D+ K-S 0.05

0.9504 0.04718 PRUEBA KOLMOGOR

1213.2600

X-VALOR MEDIO

(X-VALOR MEDIO)2

XI

5.54

-4.5400

20.6116

1

2.85

-4.5400

20.6116

2

1

-4.5400

20.6116

3

10

-4.5400

20.6116

4

9

-4.5400

20.6116

5

150

-4.5400

20.6116

6

8

-4.5400

20.6116

7

12.2474

-4.5400

1.1001 831

Fo(X/N)

FoAcum

F(x) Acum

1 0.0012 1 0.0012

0.0012

0.1813

0.0024

0.3297

1 0.0012 1 0.0012

0.0036

0.4512

0.0048

0.5507

1 0.0012 1 0.0012

0.0060

0.6321

0.0072

0.6988

0.0084

0.7534

20.6116

8

1 0.0012 1 0.0012

0.0096

0.7981

-4.5400 -4.5400

20.6116 20.6116

0.0108 0.0120

0.8347 0.8647

0.04718

-4.5400

20.6116

0.0132

0.8892

0.9504

-4.5400

20.6116

9 1 0.0012 10 1 0.0012 11 1 0.0012 12 1 0.0012

0.0144

0.9093

-4.5400

20.6116

0.0156

0.9257

-3.5400

12.5316

0.0181

0.9392

-3.5400

12.5316

13 1 0.0012 14 2 0.0024 15 2 0.0024

0.0205

0.9502

-3.5400

12.5316

0.0229

0.9592

-3.5400

12.5316

16 2 0.0024 17 2 0.0024

0.0253

0.9666

-3.5400 -3.5400

12.5316 12.5316

0.0277 0.0301

0.9727 0.9776

-3.5400

12.5316

18 2 0.0024 19 2 0.0024 20 2 0.0024

0.0325

0.9817

-3.5400

12.5316

0.0349

0.9850

-3.5400

12.5316

0.0373

0.9877

-3.5400

12.5316

21 2 0.0024 22 2 0.0024 23 2 0.0024

0.0397

0.9899

-3.5400

12.5316

0.0421

0.9918

-3.5400

12.5316

0.0445

0.9933

-3.5400

12.5316

24 2 0.0024 25 2 0.0024 26 2 0.0024

0.0469

0.9945

-3.5400

12.5316

0.0493

0.9955

-3.5400

12.5316

0.0517

0.9963

-2.5400

6.4516

27 2 0.0024 28 2 0.0024 29 3 0.0036

0.0554

0.9970

X

-2.5400

6.4516

30 3 0.0036 31 3 0.0036 32 3 0.0036

0.0590

0.9975

-2.5400

6.4516

0.0626

0.9980

-2.5400

6.4516

0.0662

0.9983

-2.5400

6.4516

33 3 0.0036 34 3 0.0036 35 3 0.0036

0.0698

0.9986

-2.5400

6.4516

0.0734

0.9989

-2.5400

6.4516

0.0770

0.9991

-2.5400

6.4516

36 3 0.0036 37 3 0.0036 38 3 0.0036

0.0806

0.9993

-2.5400

6.4516

0.0842

0.9994

-2.5400

6.4516

0.0878

0.9995

-2.5400

6.4516

39 3 0.0036 40 3 0.0036 41 3 0.0036

0.0915

0.9996

-2.5400

6.4516

0.0951

0.9997

-2.5400

6.4516

0.0987

0.9997

-2.5400

6.4516

42 3 0.0036 43 3 0.0036 44 3 0.0036

0.1023

0.9998

-2.5400

6.4516

0.1059

0.9998

-2.5400

6.4516

0.1095

0.9998

-1.5400 -1.5400

2.3716 2.3716

45 4 0.0048 46 4 0.0048 47 4 0.0048

0.1143 0.1191

0.9999 0.9999

-1.5400

2.3716

0.1239

0.9999

-1.5400

2.3716

48 4 0.0048 49 4 0.0048 50 4 0.0048

0.1288

0.9999

-1.5400

2.3716

0.1336

0.9999

-1.5400

2.3716

0.1384

1.0000

-1.5400

2.3716

51 4 0.0048 52 4 0.0048 53 4 0.0048

0.1432

1.0000

-1.5400

2.3716

0.1480

1.0000

-1.5400

2.3716

0.1528

1.0000

-1.5400

2.3716

54 4 0.0048 55 4 0.0048 56 4 0.0048

0.1576

1.0000

-1.5400

2.3716

0.1625

1.0000

-1.5400

2.3716

0.1673

1.0000

-1.5400

2.3716

57 4 0.0048 58 4 0.0048 59 4 0.0048

0.1721

1.0000

-1.5400

2.3716

0.1769

1.0000

-1.5400

2.3716

0.1817

1.0000

-1.5400

2.3716

0.1865

1.0000

0.1925

1.0000

0.2916

60 4 0.0048 61 5 0.0060 62 5 0.0060

-0.5400

0.2916

-0.5400

0.1986

1.0000

-0.5400

0.2916

63 5 0.0060

0.2046

1.0000

-0.5400 -0.5400

0.2916 0.2916

64 5 0.0060 65 5 0.0060

0.2106 0.2166

1.0000 1.0000

-0.5400

0.2916

-0.5400

0.2916

-0.5400

0.2916

-0.5400

0.2916

-0.5400

0.2916

-0.5400

0.2916

-0.5400

0.2916

-0.5400

0.2916

-0.5400

0.2916

-0.5400

0.2916

-0.5400

0.2916

-0.5400

0.2916

0.4600

0.2116

0.4600

0.2116

0.4600

0.2116

0.4600 0.4600

0.2116 0.2116

0.4600

0.2116

0.4600

0.2116

0.4600

0.2116

0.4600

0.2116

0.4600

0.2116

0.4600

0.2116

0.4600

0.2116

1.4600

2.1316

1.4600

2.1316

1.4600

2.1316

1.4600

2.1316

1.4600

2.1316

1.4600

2.1316

1.4600

2.1316

1.4600

2.1316

1.4600

66 5 0.0060 67 5 0.0060 68 5 0.0060

0.2226

1.0000

0.2286

1.0000

0.2347

1.0000

69 5 0.0060 70 5 0.0060 71 5 0.0060

0.2407

1.0000

0.2467

1.0000

0.2527

1.0000

72 5 0.0060 73 5 0.0060 74 5 0.0060

0.2587

1.0000

0.2647

1.0000

0.2708

1.0000

75 5 0.0060 76 5 0.0060 77 5 0.0060

0.2768

1.0000

0.2828

1.0000

0.2888

1.0000

78 6 0.0072 79 6 0.0072 80 6 0.0072

0.2960

1.0000

0.3032

1.0000

0.3105

1.0000

0.3177 0.3249

1.0000 1.0000

0.3321

1.0000

0.3394

1.0000

0.3466

1.0000

0.3538

1.0000

0.3610

1.0000

0.3682

1.0000

0.3755

1.0000

0.3839

1.0000

0.3923

1.0000

0.4007

1.0000

0.4091

1.0000

0.4176

1.0000

0.4260

1.0000

0.4344

1.0000

81 6 0.0072 82 6 0.0072 83 6 0.0072 84 6 0.0072 85 6 0.0072 86 6 0.0072 87 6 0.0072 88 6 0.0072 89 6 0.0072 90 7 0.0084 91 7 0.0084 92 7 0.0084 93 7 0.0084 94 7 0.0084 95 7 0.0084

0.4428

1.0000

2.1316

96 7 0.0084 97 7 0.0084 98 7 0.0084

0.4513

1.0000

1.4600

2.1316

99 7 0.0084

0.4597

1.0000

1.4600 1.4600

2.1316 2.1316

100 7 0.0084 101 7 0.0084

0.4681 0.4765

1.0000 1.0000

1.4600

2.1316

2.4600

6.0516

2.4600

6.0516

2.4600

6.0516

2.4600

6.0516

2.4600

6.0516

2.4600

6.0516

2.4600

6.0516

2.4600

6.0516

2.4600

6.0516

2.4600

6.0516

2.4600

6.0516

2.4600

6.0516

2.4600

6.0516

2.4600

6.0516

2.4600 2.4600

6.0516 6.0516

2.4600

6.0516

2.4600

6.0516

2.4600

6.0516

3.4600

11.9716

3.4600

11.9716

3.4600

11.9716

3.4600

11.9716

3.4600

11.9716

3.4600

11.9716

3.4600

11.9716

3.4600

11.9716

3.4600

11.9716

3.4600

11.9716

3.4600

11.9716

3.4600

11.9716

3.4600

102 7 0.0084 103 8 0.0096 104 8 0.0096 105 8 0.0096 106 8 0.0096 107 8 0.0096 108 8 0.0096 109 8 0.0096 110 8 0.0096 111 8 0.0096 112 8 0.0096 113 8 0.0096 114 8 0.0096 115 8 0.0096 116 8 0.0096 117 8 0.0096 118 8 0.0096 119 8 0.0096 120 8 0.0096 121 8 0.0096 122 9 0.0108 123 9 0.0108 124 9 0.0108 125 9 0.0108 126 9 0.0108 127 9 0.0108 128 9 0.0108 129 9 0.0108 130 9 0.0108 131 9 0.0108

0.4850

1.0000

0.4946

1.0000

0.5042

1.0000

0.5138

1.0000

0.5235

1.0000

0.5331

1.0000

0.5427

1.0000

0.5523

1.0000

0.5620

1.0000

0.5716

1.0000

0.5812

1.0000

0.5909

1.0000

0.6005

1.0000

0.6101

1.0000

0.6197

1.0000

0.6294 0.6390

1.0000 1.0000

0.6486

1.0000

0.6582

1.0000

0.6679

1.0000

0.6787

1.0000

0.6895

1.0000

0.7004

1.0000

0.7112

1.0000

0.7220

1.0000

0.7329

1.0000

0.7437

1.0000

0.7545

1.0000

0.7653

1.0000

0.7762

1.0000

0.7870

1.0000

0.7978

1.0000

11.9716

132 9 0.0108 133 9 0.0108 134 9 0.0108

0.8087

1.0000

3.4600

11.9716

135 9 0.0108

0.8195

1.0000

4.4600 4.4600

19.8916 19.8916

136 10 0.0120 137 10 0.0120

0.8315 0.8436

1.0000 1.0000

4.4600

19.8916

4.4600

19.8916

4.4600

19.8916

4.4600

19.8916

4.4600

19.8916

4.4600

19.8916

4.4600

19.8916

4.4600

19.8916

4.4600

19.8916

4.4600

19.8916

4.4600

19.8916

4.4600 4.4600

138 10 0.0120 139 10 0.0120 140 10 0.0120 141 10 0.0120 142 10 0.0120 143 10 0.0120 144 10 0.0120 145 10 0.0120 146 10 0.0120

0.8556

1.0000

0.8676

1.0000

0.8797

1.0000

0.8917

1.0000

0.9037

1.0000

0.9158

1.0000

0.9278

1.0000

0.9398

1.0000

0.9519

1.0000

0.9639

1.0000

0.9759

1.0000

19.8916

147 10 0.0120 148 10 0.0120 149 10 0.0120

0.9880

1.0000

19.8916

150

1.0000

1.0000

150

10 0.0120 831

CHI CALCULADO CHI TABLA OV -SMIRNOV /Fo Acum-F(x) Acum/

PRUEBA C CONCLUSION

0.1801

XI

FoAcum

F(x)

0.0012

0.1637

0.0024

0.1341

1 0.0012 1 0.0012

0.0036

0.1098

0.0048

0.0899

1 0.0012 1 0.0012

0.0060

0.0736

0.0072

0.0602

1 0.0012 1 0.0012

0.0084

0.0493

0.0096

0.0404

0.0108 0.0120

0.0331 0.0271

0.0132

0.0222

0.0144

0.0181

0.0156

0.0149

0.0181

0.0122

0.0205

0.0100

0.0229

0.0082

0.0253

0.0067

0.0277 0.0301

0.0055 0.0045

0.0325

0.0037

0.0349

0.0030

0.0373

0.0025

0.0397

0.0020

0.0421

0.0016

0.0445

0.0013

0.0469

0.0011

0.0493

0.0009

0.0517

0.0007

0.0554

0.0006

X

Fo

1

2

3

4

0.6261

5

0.6916

6

0.7450

7

0.7885

8

0.8239 0.8526

9 1 0.0012 10 1 0.0012 11 1 0.0012 12 1 0.0012

0.3273 0.4476 0.5459

0.8760 0.8948 0.9101 0.9211 0.9298 0.9364 0.9414 0.9450 0.9475 0.9492 0.9501 0.9504 0.9502 0.9497 0.9487 0.9476 0.9461 0.9446 0.9416

351 177.

NO SE AJUSTA A UNA DISTRIBUCION EXPONENCIAL

1 0.0012 1 0.0012

13 1 0.0012 14 2 0.0024 15 2 0.0024 16 2 0.0024 17 2 0.0024 18 2 0.0024 19 2 0.0024 20 2 0.0024 21 2 0.0024 22 2 0.0024 23 2 0.0024 24 2 0.0024 25 2 0.0024 26 2 0.0024 27 2 0.0024 28 2 0.0024 29 3 0.0036

0.9386 0.9354 0.9322 0.9288 0.9255 0.9221 0.9186 0.9152 0.9117 0.9081 0.9046 0.9010 0.8975 0.8939 0.8903 0.8856 0.8808 0.8760 0.8712 0.8664 0.8616 0.8568 0.8520 0.8471 0.8423 0.8375 0.8327 0.8279 0.8231 0.8183 0.8135

30 3 0.0036 31 3 0.0036 32 3 0.0036 33 3 0.0036 34 3 0.0036 35 3 0.0036 36 3 0.0036 37 3 0.0036 38 3 0.0036 39 3 0.0036 40 3 0.0036 41 3 0.0036 42 3 0.0036 43 3 0.0036 44 3 0.0036 45 4 0.0048 46 4 0.0048 47 4 0.0048 48 4 0.0048 49 4 0.0048 50 4 0.0048 51 4 0.0048 52 4 0.0048 53 4 0.0048 54 4 0.0048 55 4 0.0048 56 4 0.0048 57 4 0.0048 58 4 0.0048 59 4 0.0048

0.0590

0.0005

0.0626

0.0004

0.0662

0.0003

0.0698

0.0003

0.0734

0.0002

0.0770

0.0002

0.0806

0.0001

0.0842

0.0001

0.0878

0.0001

0.0915

0.0001

0.0951

0.0001

0.0987

0.0001

0.1023

0.0000

0.1059

0.0000

0.1095

0.0000

0.1143 0.1191

0.0000 0.0000

0.1239

0.0000

0.1288

0.0000

0.1336

0.0000

0.1384

0.0000

0.1432

0.0000

0.1480

0.0000

0.1528

0.0000

0.1576

0.0000

0.1625

0.0000

0.1673

0.0000

0.1721

0.0000

0.1769

0.0000

0.1817

0.0000

0.1865

0.0000

0.1925

0.0000

0.8014

60 4 0.0048 61 5 0.0060 62 5 0.0060

0.1986

0.0000

0.7954

63 5 0.0060

0.2046

0.0000

0.7894 0.7834

64 5 0.0060 65 5 0.0060

0.2106 0.2166

0.0000 0.0000

0.8075

0.7774 0.7714 0.7653 0.7593 0.7533 0.7473 0.7413 0.7353 0.7292 0.7232 0.7172 0.7112 0.7040 0.6968 0.6895 0.6823 0.6751 0.6679 0.6606 0.6534 0.6462 0.6390 0.6318 0.6245 0.6161 0.6077 0.5993 0.5909 0.5824 0.5740 0.5656

66 5 0.0060 67 5 0.0060 68 5 0.0060 69 5 0.0060 70 5 0.0060 71 5 0.0060 72 5 0.0060 73 5 0.0060 74 5 0.0060 75 5 0.0060 76 5 0.0060 77 5 0.0060 78 6 0.0072 79 6 0.0072 80 6 0.0072 81 6 0.0072 82 6 0.0072 83 6 0.0072 84 6 0.0072 85 6 0.0072 86 6 0.0072 87 6 0.0072 88 6 0.0072 89 6 0.0072 90 7 0.0084 91 7 0.0084 92 7 0.0084 93 7 0.0084 94 7 0.0084 95 7 0.0084

0.2226

0.0000

0.2286

0.0000

0.2347

0.0000

0.2407

0.0000

0.2467

0.0000

0.2527

0.0000

0.2587

0.0000

0.2647

0.0000

0.2708

0.0000

0.2768

0.0000

0.2828

0.0000

0.2888

0.0000

0.2960

0.0000

0.3032

0.0000

0.3105

0.0000

0.3177 0.3249

0.0000 0.0000

0.3321

0.0000

0.3394

0.0000

0.3466

0.0000

0.3538

0.0000

0.3610

0.0000

0.3682

0.0000

0.3755

0.0000

0.3839

0.0000

0.3923

0.0000

0.4007

0.0000

0.4091

0.0000

0.4176

0.0000

0.4260

0.0000

0.4344

0.0000

0.4428

0.0000

0.5487

96 7 0.0084 97 7 0.0084 98 7 0.0084

0.4513

0.0000

0.5403

99 7 0.0084

0.4597

0.0000

0.5319 0.5235

100 7 0.0084 101 7 0.0084

0.4681 0.4765

0.0000 0.0000

0.5572

0.5150 0.5054 0.4958 0.4862 0.4765 0.4669 0.4573 0.4477 0.4380 0.4284 0.4188 0.4091 0.3995 0.3899 0.3803 0.3706 0.3610 0.3514 0.3418 0.3321 0.3213 0.3105 0.2996 0.2888 0.2780 0.2671 0.2563 0.2455 0.2347 0.2238 0.2130

102 7 0.0084 103 8 0.0096 104 8 0.0096 105 8 0.0096 106 8 0.0096 107 8 0.0096 108 8 0.0096 109 8 0.0096 110 8 0.0096 111 8 0.0096 112 8 0.0096 113 8 0.0096 114 8 0.0096 115 8 0.0096 116 8 0.0096 117 8 0.0096 118 8 0.0096 119 8 0.0096 120 8 0.0096 121 8 0.0096 122 9 0.0108 123 9 0.0108 124 9 0.0108 125 9 0.0108 126 9 0.0108 127 9 0.0108 128 9 0.0108 129 9 0.0108 130 9 0.0108 131 9 0.0108

0.4850

0.0000

0.4946

0.0000

0.5042

0.0000

0.5138

0.0000

0.5235

0.0000

0.5331

0.0000

0.5427

0.0000

0.5523

0.0000

0.5620

0.0000

0.5716

0.0000

0.5812

0.0000

0.5909

0.0000

0.6005

0.0000

0.6101

0.0000

0.6197

0.0000

0.6294 0.6390

0.0000 0.0000

0.6486

0.0000

0.6582

0.0000

0.6679

0.0000

0.6787

0.0000

0.6895

0.0000

0.7004

0.0000

0.7112

0.0000

0.7220

0.0000

0.7329

0.0000

0.7437

0.0000

0.7545

0.0000

0.7653

0.0000

0.7762

0.0000

0.7870

0.0000

0.7978

0.0000

0.1913

132 9 0.0108 133 9 0.0108 134 9 0.0108

0.8087

0.0000

0.1805

135 9 0.0108

0.8195

0.0000

0.1685

136 10 0 0..0120 137 10 0. 0.0120

0.8315

0.0000

0.8436

0.0000

0.2022

0.1564

0.1444 0.1324 0.1203 0.1083 0.0963 0.0842 0.0722 0.0602 0.0481 0.0361

138 10 0 0..0120 139 10 0. 0.0120 140 10 0. 0.0120 141 10 0 0..0120 142 10 0. 0.0120 143 10 0. 0.0120 144 10 0 0..0120 145 10 0. 0.0120 146 10 0. 0.0120

0.8556

0.0000

0.8676

0.0000

0.8797

0.0000

0.8917

0.0000

0.9037

0.0000

0.9158

0.0000

0.9278

0.0000

0.9398

0.0000

0.9519

0.0000

0.9639

0.0000

0.9759

0.0000

0.0120

147 10 0 0..0120 148 10 0. 0.0120 149 10 0. 0.0120

0.9880

0.0000

0.0000

150

1.0000

0.0000

0.0241

150

0.0120 10 0. 831

7293836173 89749986549 HI CUADRADO DATOS SEGUN EXPONENCIALL (Ei) EXPONENCIA

(X-Ei)^2/Ei

136.0731

134

111.4072

109

91.2125

89

74.6785

73

61.1416

59

50.0585

48

40.9844

39

33.5552

32

27.4727 22.4927

26 21

18.4155

16

15.0773

13

12.3443

10

10.1066

7

8.2746

5

6.7747

3

5.5466

2

4.5412 3.7180

1 1

3.0441

0

2.4923

0

2.0405

0

1.6706

0

1.3678

0

1.1198

1

0.9169

1

0.7507

2

0.6146

3

0.5032

12

CONCLUSION

NO SE AJUSTA A UNA DISTRIBUCION EXPONENCIAL

0.4120

16

0.3373

21

0.2762

27

0.2261

34

0.1851

43

0.1516

54

0.1241

67

0.1016

83

0.0832

102

0.0681

126

0.0558

155

0.0456

191

0.0374

235

0.0306

288

0.0251

353

0.0205 0.0168

772 945

0.0137

1156

0.0113

1413

0.0092

1728

0.0075

2112

0.0062

2582

0.0051

3155

0.0041

3856

0.0034

4711

0.0028

5756

0.0023

7032

0.0019

8591

0.0015

10495

0.0012

12820

0.0010

15660

0.0008

29892

0.0007

36513

0.0006

44599

0.0005

54475

0.0004

66538

0.0003

81272

0.0003

99268

0.0002

121249

0.0002

148096

0.0001

180887

0.0001

220938

0.0001

269857

0.0001

329606

0.0001

402584

0.0001

491719

0.0000

600590

0.0000

733564

0.0000

1290213

0.0000

1575872

0.0000

1924777

0.0000 0.0000

2350931 2871436

0.0000

3507183

0.0000

4283685

0.0000

5232108

0.0000

6390513

0.0000

7805393

0.0000

9533532

0.0000

11644285

0.0000

19358220

0.0000

23644186

0.0000

28879078

0.0000

35272988

0.0000

43082528

0.0000

52621122

0.0000

64271586

0.0000

78501496

0.0000

95881947

0.0000

117110477

0.0000

143039063

0.0000

174708309

0.0000

213389214

0.0000

340420152

0.0000

415790116

0.0000

507847198

0.0000

620285972

0.0000

757619001

0.0000

925357941

0.0000

1130234745

0.0000

1380471838

0.0000

1686112114

0.0000

2059421990

0.0000

2515383703

0.0000

3072296596

0.0000

3752511540

0.0000

4583327948

0.0000 0.0000

5598089401 6837521838

0.0000

8351368036

0.0000

###

0.0000

###

0.0000

###

0.0000

###

0.0000

###

0.0000

###

0.0000

###

0.0000

###

0.0000

###

0.0000

###

0.0000

###

0.0000

###

0.0000

###

0.0000

###

0.0000

###

0.0000

###

0.0000

###

0.0000

###

0.0000

###

0.0000

###

0.0000

###

0.0000

###

0.0000

###

0.0000

###

0.0000

###

0.0000

###

0.0000

###

0.0000

###

0.0000

###

0.0000

###

0.0000

###

MUESTRA 2 Este gráfico no está disponible en su versión de Excel. Si edita esta forma o guarda el libro en un formato f ormato de archivo diferente, el gráfico no se podrá utilizar.

NUMEROS ALEATORIOS

1 2 3 4 5 6 7 8 9

-21.22969 -9.21443 -4.74790 -2.31594 1.18129 1.48481 2.52667 3.33981 3.87637

100 NUMERO ALEATORIOS

12 1 2 74 114 39 24 68 103

110

-21.22969 -9.21443 -4.74790 -2.31594 1.18129 1.48481 2.52667 8 3.33981 9 3.87637

14

1 2 3 4 5 6 7

10 11 12 13 14 15 16 17 18 19 20

3.88250 3.96291 4.49292 4.68007 4.94304 5.41704 5.92962 7.42803 8.49098 8.63039 9.19640

10 11 12 13 14 15 16 17 18 19 20

3.88250 3.96291 4.49292 4.68007 4.94304 5.41704 5.92962 7.42803 8.49098 8.63039 9.19640

12 109 39 51 1 4 30 14 63 86 101

21 22 23 24 25 26 27 28 29 30 31

9.32996 10.96412 11.93069 13.58003 13.64816 14.09902 15.73829 16.20990 16.23385 16.48123 16.95416

21 22 23 24 25 26 27 28 29 30 31

9.32996 10.96412 11.93069 13.58003 13.64816 14.09902 15.73829 16.20990 16.23385 16.48123 16.95416

18 95 38 13 70 1 112 34 29 80 5

32 33 34

17.26201 17.36072 18.09135

32 33 34

17.26201 17.36072 18.09135

95 5 31

MEDIA

29.42759

35 36 37 38 39 40 41

18.14747 18.25659 18.42881 18.80067 18.95511 19.24480 19.29858

35 36 37 38 39 40 41

18.14747 18.25659 18.42881 18.80067 18.95511 19.24480 19.29858

26 82 113 70 93 46 68

42 43 44 45 46 47 48 49 50 51 52

19.36428 19.41322 19.95754 20.10091 20.20132 21.27515 21.36244 21.55509 22.08667 22.43696 23.21174

42 43 44 45 46 47 48 49 50 51 52

19.36428 19.41322 19.95754 20.10091 20.20132 21.27515 21.36244 21.55509 22.08667 22.43696 23.21174

13 83 89 111 90 32 102 107 7 82 38

53 54 55 56 57 58 59 60 61 62 63

23.28943 24.89292 25.29962 25.39793 25.47812 25.74927 26.06687 26.35455 26.43369 26.53221 26.56906

53 54 55 56 57 58 59 60 61 62 63

23.28943 24.89292 25.29962 25.39793 25.47812 25.74927 26.06687 26.35455 26.43369 26.53221 26.56906

0 46 55 96 84 67 101 22 45 32 89

64 65 66 67 68 69 70 71 72 73 74

26.84435 26.86131 27.19138 27.30291 27.31790 27.79630 27.87094 28.09351 28.11489 28.12486 28.69402

64 65 66 67 68 69 70 71 72 73 74

26.84435 26.86131 27.19138 27.30291 27.31790 27.79630 27.87094 28.09351 28.11489 28.12486 28.69402

29 49 13 53 32 109 27 59 85 61 111

75 76 77



28.76426 29.00226 29.03898

75 76 77

   28.76426 29.00226 29.03898

107 101 75

78 79 80 81 82 83 84

29.40995 29.53365 30.31543 30.39553 31.12128 31.36254 31.48280

78 79 80 81 82 83 84

29.40995 29.53365 30.31543 30.39553 31.12128 31.36254 31.48280

63 52 69 100 78 110 64

85 86 87 88 89 90 91 92 93 94 95

32.25197 32.32044 32.35094 32.82525 32.85831 33.48118 33.62631 33.78083 34.41134 34.50249 34.51615

85 86 87 88 89 90 91 92 93 94 95

32.25197 32.32044 32.35094 32.82525 32.85831 33.48118 33.62631 33.78083 34.41134 34.50249 34.51615

12 110 41 70 59 111 70 106 4 92 28

96 97 98 99 100 101 102 103 104 105 106

34.51889 34.96212 35.05767 35.26272 35.27350 35.50507 35.78715 35.82930 36.36172 36.55877 37.26089

96 97 98 99 100 101 102 103 104 105 106

34.51889 34.96212 35.05767 35.26272 35.27350 35.50507 35.78715 35.82930 36.36172 36.55877 37.26089

67 90 57 113 112

107 108 109 110 111 112 113 114 115 116 117

37.59586 38.20520 38.23694 38.30689 38.54933 39.30117 39.73604 40.83861 41.05007 41.30661 41.89643

107 108 109 110 111 112 113 114 115 116 117

37.59586 38.20520 38.23694 38.30689 38.54933 39.30117 39.73604 40.83861 41.05007 41.30661 41.89643

118 119 120



41.97724 42.26109 42.81079

118 41.97724 119 42.26109 120 42.81079

121 122 123 124 125 126 127

42.98591 43.40122 44.06374 44.13974 45.51438 46.62674 46.90667

121 122 123 124 125 126 127

42.98591 43.40122 44.06374 44.13974 45.51438 46.62674 46.90667

128 129 130 131 132 133 134 135 136 137 138

47.03629 47.32482 47.86308 48.30382 48.54479 48.77250 49.46972 50.66052 50.96819 52.29378 52.86910

128 129 130 131 132 133 134 135 136 137 138

47.03629 47.32482 47.86308 48.30382 48.54479 48.77250 49.46972 50.66052 50.96819 52.29378 52.86910

139 140 141 142 143 144 145 146 147 148 149

53.16553 53.48650 54.66736 56.74874 57.14406 60.29815 61.56703 63.09349 63.16666 66.80724 67.99673

139 140 141 142 143 144 145 146 147 148 149

53.16553 53.48650 54.66736 56.74874 57.14406 60.29815 61.56703 63.09349 63.16666 66.80724 67.99673

150

78.23795

150 78.23795

PRUEBA DE CORRIDAS S

# DE CORRIDAS

1 1 1 1 1 1 1

1 0 0 0 0 0 0

1 1

0 0

1 1 1 1 1 1 1 1 1 1 1

0 0 0 0 0 0 0 0 0 0 0

1 1 1 1 1 1 1 1 1 1 1

0 0 0 0 0 0 0 0 0 0 0

1 1 1

0 0 0

Co n ALFA n1 n2 VALOR ESPERADO VARIANZA ESTADISTICO

2 150 0.05 72 78 75.88 37.13 12.12477

VALOR EN TABLAS 1.95996

CONCLUSION

LOS DATOS NO SON INDEPENDIENTES

1 1 1 1 1 1 1

0 0 0 0 0 0 0

1 1 1 1 1 1 1 1 1 1 1

0 0 0 0 0 0 0 0 0 0 0

1 1 1 1 1 1 1 1 1 1 1

0 0 0 0 0 0 0 0 0 0 0

1 1 1 1 1 1 1 1 1 1 1

0 0 0 0 0 0 0 0 0 0 0

1 1 1

0 0 0

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

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

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0

0 0 0

0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0

0

0

Nivel de signifcancia:

0.05

SUMAMEDIO)2 DE (X-VALOR

41991.3137

X-VALOR MEDIO

(X-VALOR MEDIO)2

XI

MEDIA 29.427588 16.79 DESVIACION MINIMO -21 MAXIMO 78 RANGO 99 n 150 # INTERVALOS 8

-50.6573 -38.6420 -34.1755 -31.7435 -28.2463 -27.9428 -26.9009

2566.1600 1493.2052 1167.9643 1007.6517 797.8535 780.7987 723.6594

1 2 3 4 5 6 7

-26.0878

68 680.5723

8

12.1582

-25.5512

652.8648

9

4414.13821 0.02047 0.2524

-25.5451 -25.4647 -24.9347 -24.7475 -24.4846 -24.0106 -23.4980 -21.9996 -20.9366 -20.7972 -20.2312

652.5516 648.4500 621.7374 61 612.4397 599.4933 576.5065 552.1547 483.9805 438.3416 432.5233 409.3008

10 11 12 13 14 15 16 17 18 19 20

3.88250 3.96291 4.49292 4.68007 4.94304 5.41704 5.92962 7.42803 8.49098 8.63039 9.19640

-20.0976 -18.4635 -17.4969 -15.8476 -15.7794 -15.3286 -13.6893 -13.2177 -13.1937 -12.9464 -12.4734

403.9149 340.8998 306.1415 251.1452 248.9904 234.9649 187.3968 174.7073 174.0747 167.6082 155.5865

21 22 23 24 25 26 27 28 29 30 31

9.32996 10.96412 11.93069 13.58003 13.64816 14.09902 15.73829 16.20990 16.23385 16.48123 16.95416

-12.1656 -12.0669 -11.3362

148.0012 145.6093 128.5103

32 33 34

17.26201 17.36072 18.09135

INTERVALOS RAIZ de n 12.2474 TAMAÑO INTERVALO N K-S D+ LAMBDA (λ)

99.4009953

X

-21.22969 -9.21443 -4.74790 -2.31594 1.18129 1.48481 2.52667 3.33981 3.87637

42 43 44 45 46 47 48 49 50 51 52

18.14747 18.25659 18.42881 18.80067 18.95511 19.24480 19.29858 19.36428 19.41322 19.95754 20.10091 20.20132 21.27515 21.36244 21.55509 22.08667 22.43696 23.21174

37.6769 20.5632 17.0401 16.2382 15.5983 13.5301 11.2944 9.4435 8.9634 8.3832 8.1712

53 54 55 56 57 58 59 60 61 62 63

23.28943 24.89292 25.29962 25.39793 25.47812 25.74927 26.06687 26.35455 26.43369 26.53221 26.56906

-2.5832 -2.5663 -2.2362 -2.1247 -2.1097 -1.6313 -1.5566 -1.3341 -1.3127 -1.3027 -0.7336

6.6731 6.5858 5.0006 4.5143 4.4508 2.6611 2.4232 1.7798 1.7232 1.6971 0.5381

64 65 66 67 68 69 70 71 72 73 74

26.84435 26.86131 27.19138 27.30291 27.31790 27.79630 27.87094 28.09351 28.11489 28.12486 28.69402

-0.6633 -0.4253 -0.3886

0.4400 0.1809 0.1510

75 76 77

28.76426 29.00226 29.03898

-11.2801 -11.1710 -10.9988 -10.6269 -10.4725 -10.1828 -10.1290

127.2411 124.7912 120.9731 112.9313 109.6728 103.6891 102.5968

35 36 37 38 39 40 41

-10.0633 -10.0144 -9.4700 -9.3267 -9.2263 -8.1524 -8.0652 -7.8725 -7.3409 -6.9906 -6.2158

101.2702 100.2876 89.6818 86.9869 85.1241 66.4623 65.0467 61.9762 53.8891 48.8688 38.6367

-6.1382 -4.5347 -4.1280 -4.0297 -3.9495 -3.6783 -3.3607 -3.0730 -2.9939 -2.8954 -2.8585

85 86 87 88 89 90 91 92 93 94 95

29.40995 29.53365 30.31543 30.39553 31.12128 31.36254 31.48280 32.25197 32.32044 32.35094 32.82525 32.85831 33.48118 33.62631 33.78083 34.41134 34.50249 34.51615

25.9214 30.6311 31.6979 34.0487 34.1747 36.9357 40.4440 40.9820 48.0823 50.8537 61.3606

96 97 98 99 100 101 102 103 104 105 106

34.51889 34.96212 35.05767 35.26272 35.27350 35.50507 35.78715 35.82930 36.36172 36.55877 37.26089

8.1683 8.7776 8.8094 8.8793 9.1217 9.8736 10.3085 11.4110 11.6225 11.8790 12.4688

66.7207 77.0465 77.6047 78.8420 83.2061 97.4876 106.2642 130.2115 135.0820 141.1112 155.4720

107 108 109 110 111 112 113 114 115 116 117

37.59586 38.20520 38.23694 38.30689 38.54933 39.30117 39.73604 40.83861 41.05007 41.30661 41.89643

12.5496 12.8335 13.3832

157.4936 164.6989 179.1100

118 41.97724 119 42.26109 120 42.81079

-0.0176 0.1061 0.8878 0.9679 1.6937 1.9350 2.0552

0.0003 0.0112 0.7883 0.9369 2.8686 3.7440 4.2239

78 79 80 81 82 83 84

2.8244 2.8929 2.9233 3.3977 3.4307 4.0536 4.1987 4.3532 4.9837 5.0749 5.0886

7.9771 8.3686 8.5460 11.5441 11.7698 16.4316 17.6293 18.9507 24.8377 25.7546 25.8935

5.0913 5.5345 5.6301 5.8351 5.8459 6.0775 6.3596 6.4017 6.9341 7.1312 7.8333

128 129 130 131 132 133 134 135 136 137 138

42.98591 43.40122 44.06374 44.13974 45.51438 46.62674 46.90667 47.03629 47.32482 47.86308 48.30382 48.54479 48.77250 49.46972 50.66052 50.96819 52.29378 52.86910

563.4901 578.8312 637.0459 746.4456 768.2031 952.9918 1032.9439 1133.3931 1138.3247 1397.2385 1487.5789

139 140 141 142 143 144 145 146 147 148 149

53.16553 53.48650 54.66736 56.74874 57.14406 60.29815 61.56703 63.09349 63.16666 66.80724 67.99673

2382.4517

150 78.23795 150 4414.1382061

13.5583 13.9736 14.6361 14.7121 16.0868 17.1992 17.4791

183.8282 195.2625 214.2168 216.4473 258.7849 295.8108 305.5185

121 122 123 124 125 126 127

17.6087 17.8972 18.4355 18.8762 19.1172 19.3449 20.0421 21.2329 21.5406 22.8662 23.4415

310.0663 320.3107 339.8673 356.3123 365.4675 374.2255 401.6869 450.8375 463.9977 522.8629 549.5046

23.7379 24.0589 25.2398 27.3212 27.7165 30.8706 32.1394 33.6659 33.7391 37.3797 38.5691 48.8104

D+

0.2524

K-S

0.02047

PRUEBA KOLMOGOROV -SMIRNOV Fo(X/N)

FoAcum

F(x) Acum

/Fo Acum-F(x) Acum/

-0.0048 -0.0021 -0.0011 -0.0005 0.0003 0.0003 0.0006

-0.0048 -0.0069 -0.0080 -0.0085 -0.0082 -0.0079 -0.0073

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0048 0.0069 0.0080 0.0085 0.0082 0.0079 0.0073

0.0008

-0.0066

0.0000

0.0066

8

0.0009

-0.0057

0.0000

0.0057

0.0009 0.0009 0.0010 0.0011 0.0011 0.0012 0.0013 0.0017 0.0019 0.0020 0.0021

-0.0048 -0.0039 -0.0029 -0.0018 -0.0007 0.0005 0.0019 0.0035 0.0055 0.0074 0.0095

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0021 0.0025 0.0027 0.0031 0.0031 0.0032 0.0036 0.0037 0.0037 0.0037 0.0038

0.0116 0.0141 0.0168 0.0199 0.0230 0.0262 0.0297 0.0334 0.0371 0.0408 0.0447

0.0039 0.0039 0.0041

0.0486 0.0525 0.0566

CONCLUSION

NO SE AJUSTA A UNA DISTRIBUCION NORMAL

XI

X

1 -21.22969 2 -9.21443 3 -4.74790 4 -2.31594 5 1.18129 6 1.48481 7 2.52667 9

3.33981 3.87637

0.0048 0.0039 0.0029 0.0018 0.0007 0.0005 0.0019 0.0035 0.0055 0.0074 0.0095

10 11 12 13 14 15 16 17 18 19 20

3.88250 3.96291 4.49292 4.68007 4.94304 5.41704 5.92962 7.42803 8.49098 8.63039 9.19640

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0116 0.0141 0.0168 0.0199 0.0230 0.0262 0.0297 0.0334 0.0371 0.0408 0.0446

21 22 23 24 25 26 27 28 29 30 31

9.32996 10.96412 11.93069 13.58003 13.64816 14.09902 15.73829 16.20990 16.23385 16.48123 16.95416

0.0000 0.0000 0.0000

0.0485 0.0525 0.0566

32 17.26201 33 17.36072 34 18.09135

42 43 44 45 46 47 48 49 50 51 52

18.14747 18.25659 18.42881 18.80067 18.95511 19.24480 19.29858 19.36428 19.41322 19.95754 20.10091 20.20132 21.27515 21.36244 21.55509 22.08667 22.43696 23.21174

0.1411 0.1461 0.1512 0.1562 0.1610 0.1658 0.1705 0.1751 0.1794 0.1836 0.1875

53 54 55 56 57 58 59 60 61 62 63

23.28943 24.89292 25.29962 25.39793 25.47812 25.74927 26.06687 26.35455 26.43369 26.53221 26.56906

0.0175 0.0202 0.0233 0.0268 0.0307 0.0351 0.0399 0.0453 0.0513 0.0579 0.0651

0.1911 0.1945 0.1975 0.2002 0.2025 0.2045 0.2059 0.2069 0.2073 0.2070 0.2063

64 65 66 67 68 69 70 71 72 73 74

26.84435 26.86131 27.19138 27.30291 27.31790 27.79630 27.87094 28.09351 28.11489 28.12486 28.69402

0.0730 0.0817 0.0910

0.2049 0.2029 0.2001

75 28.76426 76 29.00226 77 29.03898

0.0041 0.0041 0.0042 0.0043 0.0043 0.0044 0.0044

0.0607 0.0648 0.0690 0.0733 0.0776 0.0819 0.0863

0.0001 0.0001 0.0001 0.0001 0.0002 0.0002 0.0003

0.0606 0.0648 0.0689 0.0732 0.0774 0.0817 0.0861

35 36 37 38 39 40 41

0.0044 0.0044 0.0045 0.0046 0.0046 0.0048 0.0048 0.0049 0.0050 0.0051 0.0053

0.0907 0.0951 0.0996 0.1042 0.1087 0.1136 0.1184 0.1233 0.1283 0.1334 0.1386

0.0003 0.0004 0.0005 0.0006 0.0007 0.0009 0.0011 0.0013 0.0016 0.0020 0.0024

0.0904 0.0947 0.0991 0.1036 0.1080 0.1127 0.1173 0.1219 0.1267 0.1314 0.1363

0.0053 0.0056 0.0057 0.0058 0.0058 0.0058 0.0059 0.0060 0.0060 0.0060 0.0060

0.1439 0.1495 0.1553 0.1610 0.1668 0.1726 0.1785 0.1845 0.1905 0.1965 0.2025

0.0029 0.0034 0.0041 0.0049 0.0058 0.0068 0.0081 0.0095 0.0111 0.0129 0.0151

0.0061 0.0061 0.0062 0.0062 0.0062 0.0063 0.0063 0.0064 0.0064 0.0064 0.0065

0.2086 0.2147 0.2209 0.2270 0.2332 0.2395 0.2458 0.2522 0.2586 0.2649 0.2714

0.0065 0.0066 0.0066

0.2780 0.2845 0.2911

85 86 87 88 89 90 91 92 93 94 95

29.40995 29.53365 30.31543 30.39553 31.12128 31.36254 31.48280 32.25197 32.32044 32.35094 32.82525 32.85831 33.48118 33.62631 33.78083 34.41134 34.50249 34.51615

0.0107 0.0048 0.0204 0.0362 0.0519 0.0676 0.0831 0.0983 0.1131 0.1275 0.1413

96 97 98 99 100 101 102 103 104 105 106

34.51889 34.96212 35.05767 35.26272 35.27350 35.50507 35.78715 35.82930 36.36172 36.55877 37.26089

0.6746 0.6958 0.7163 0.7361 0.7552 0.7735 0.7910 0.8077 0.8236 0.8386 0.8528

0.1546 0.1671 0.1789 0.1901 0.2004 0.2098 0.2184 0.2258 0.2324 0.2380 0.2427

107 108 109 110 111 112 113 114 115 116 117

37.59586 38.20520 38.23694 38.30689 38.54933 39.30117 39.73604 40.83861 41.05007 41.30661 41.89643

0.8660 0.8785 0.8901

0.2465 0.2493 0.2512

118 41.97724 119 42.26109 120 42.81079

0.0067 0.0067 0.0069 0.0069 0.0071 0.0071 0.0071

0.2978 0.3045 0.3113 0.3182 0.3253 0.3324 0.3395

0.1012 0.1121 0.1239 0.1365 0.1500 0.1643 0.1795

0.1966 0.1923 0.1874 0.1817 0.1753 0.1681 0.1600

78 79 80 81 82 83 84

0.0073 0.0073 0.0073 0.0074 0.0074 0.0076 0.0076 0.0077 0.0078 0.0078 0.0078

0.3468 0.3541 0.3615 0.3689 0.3763 0.3839 0.3915 0.3992 0.4070 0.4148 0.4226

0.1955 0.2124 0.2300 0.2485 0.2678 0.2877 0.3084 0.3297 0.3515 0.3738 0.3966

0.1513 0.1418 0.1314 0.1204 0.1086 0.0962 0.0832 0.0695 0.0555 0.0410 0.0260

0.0078 0.0079 0.0079 0.0080 0.0080 0.0080 0.0081 0.0081 0.0082 0.0083 0.0084

0.4305 0.4384 0.4463 0.4543 0.4623 0.4703 0.4784 0.4866 0.4948 0.5031 0.5115

0.4197 0.4431 0.4667 0.4905 0.5142 0.5379 0.5615 0.5849 0.6079 0.6306 0.6529

0.0085 0.0087 0.0087 0.0087 0.0087 0.0089 0.0090 0.0093 0.0093 0.0094 0.0095

0.5200 0.5287 0.5374 0.5460 0.5548 0.5637 0.5727 0.5819 0.5912 0.6006 0.6101

0.0095 0.0096 0.0097

0.6196 0.6292 0.6389

128 129 130 131 132 133 134 135 136 137 138

42.98591 43.40122 44.06374 44.13974 45.51438 46.62674 46.90667 47.03629 47.32482 47.86308 48.30382 48.54479 48.77250 49.46972 50.66052 50.96819 52.29378 52.86910

0.1456 0.1349 0.1237 0.1118 0.0998 0.0869 0.0736 0.0598 0.0460 0.0312 0.0162

139 140 141 142 143 144 145 146 147 148 149

53.16553 53.48650 54.66736 56.74874 57.14406 60.29815 61.56703 63.09349 63.16666 66.80724 67.99673

0.0013

150 78.23795 150 4414.1382061

0.0097 0.0098 0.0100 0.0100 0.0103 0.0106 0.0106

0.6486 0.6584 0.6684 0.6784 0.6887 0.6993 0.7099

0.9009 0.9109 0.9201 0.9286 0.9364 0.9435 0.9499

0.2523 0.2524 0.2517 0.2502 0.2476 0.2442 0.2400

121 122 123 124 125 126 127

0.0107 0.0107 0.0108 0.0109 0.0110 0.0110 0.0112 0.0115 0.0115 0.0118 0.0120

0.7206 0.7313 0.7421 0.7531 0.7641 0.7751 0.7863 0.7978 0.8094 0.8212 0.8332

0.9558 0.9611 0.9658 0.9701 0.9739 0.9773 0.9803 0.9830 0.9854 0.9874 0.9893

0.2352 0.2298 0.2237 0.2170 0.2098 0.2022 0.1940 0.1852 0.1760 0.1662 0.1561

0.0120 0.0121 0.0124 0.0129 0.0129 0.0137 0.0139 0.0143 0.0143 0.0151 0.0154

0.8452 0.8573 0.8697 0.8826 0.8955 0.9092 0.9231 0.9374 0.9517 0.9669 0.9823

0.9908 0.9922 0.9934 0.9944 0.9953 0.9961 0.9967 0.9972 0.9977 0.9981 0.9984

0.0177

1.0000

0.9987

CHI CALCULADO

146876424 177.389749986549

CHI TABLA

PRUEBA CHI CUADRADO Fo

FoAcum

F(x)

DATOS SEGUN EXPONENCIAL (Ei)

(X-Ei)^2/Ei

-0.0048 -0.0021 -0.0011 -0.0005 0.0003 0.0003 0.0006

-0.0048 -0.0069 -0.0080 -0.0085 -0.0082 -0.0079 -0.0073

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

124115838 16519935 3109920 526522 97817 110749 230639

0.0008

-0.0066

0.0000

0.0000

290841

0.0009

-0.0057

0.0000

0.0001

283779

0.0009 0.0009 0.0010 0.0011 0.0011 0.0012 0.0013 0.0017 0.0019 0.0020 0.0021

-0.0048 -0.0039 -0.0029 -0.0018 -0.0007 0.0005 0.0019 0.0035 0.0055 0.0074 0.0095

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0001 0.0001 0.0001 0.0002 0.0003 0.0003 0.0005 0.0006 0.0008 0.0011 0.0015

206923 157256 147971 117950 97005 86196 76685 89669 87617 67926 58084

0.0021 0.0025 0.0027 0.0031 0.0031 0.0032 0.0036 0.0037 0.0037 0.0037 0.0038

0.0116 0.0141 0.0168 0.0199 0.0230 0.0262 0.0297 0.0334 0.0371 0.0408 0.0447

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0019 0.0025 0.0033 0.0044 0.0057 0.0074 0.0096 0.0124 0.0159 0.0204 0.0260

45180 47322 42648 42206 32674 26820 25798 21198 16524 13284 11002

0.0039 0.0039 0.0041

0.0486 0.0525 0.0566

0.0000 0.0000 0.0000

0.0331 0.0420 0.0531

8956 7137 6128

CONCLUSION

NO SE AJUSTA A UNA DISTRIBUCION NORMAL O CONTINUA

0.0041 0.0041 0.0042 0.0043 0.0043 0.0044 0.0044 0.0044 0.0044 0.0045 0.0046 0.0046 0.0048 0.0048 0.0049 0.0050 0.0051 0.0053

0.0607 0.0648 0.0690 0.0733 0.0776 0.0819 0.0863 0.0907 0.0951 0.0996 0.1042 0.1087 0.1136 0.1184 0.1233 0.1283 0.1334 0.1386

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001 0.0001 0.0001 0.0001 0.0002 0.0002 0.0002 0.0003 0.0003 0.0004 0.0004

0.0668 0.0839 0.1048 0.1306 0.1621 0.2005 0.2471 0.3034 0.3713 0.4527 0.5501 0.6661 0.8036 0.9661 1.1573 1.3815 1.6433 1.9478

4891 3938 3203 2669 2179 1809 1469 1197 977 840 695 573 522 431 360 310 263 232

0.0053 0.0056 0.0057 0.0058 0.0058 0.0058 0.0059 0.0060 0.0060 0.0060 0.0060

0.1439 0.1495 0.1553 0.1610 0.1668 0.1726 0.1785 0.1845 0.1905 0.1965 0.2025

0.0005 0.0006 0.0007 0.0008 0.0010 0.0011 0.0013 0.0015 0.0017 0.0020 0.0023

2.3004 2.7074 3.1750 3.7102 4.3202 5.0127 5.7957 6.6772 7.6655 8.7689 9.9957

192 182 154 127 104 86 71 58 46 36 27

0.0061 0.0061 0.0062 0.0062 0.0062 0.0063 0.0063 0.0064 0.0064 0.0064 0.0065

0.2086 0.2147 0.2209 0.2270 0.2332 0.2395 0.2458 0.2522 0.2586 0.2649 0.2714

0.0026 0.0029 0.0033 0.0037 0.0041 0.0046 0.0051 0.0057 0.0063 0.0069 0.0076

11.3537 12.8505 14.4931 16.2879 18.2400 20.3537 22.6319 25.0761 27.6857 30.4587 33.3907

21 15 11 7 5 3 1 0 0 0 1

0.0065 0.0066 0.0066

0.2780 0.2845 0.2911

0.0083 0.0090 0.0098

36.4752 39.7036 43.0647

2 3 5

0.0067 0.0067 0.0069 0.0069 0.0071 0.0071 0.0071 0.0073 0.0073 0.0073 0.0074 0.0074 0.0076 0.0076 0.0077 0.0078 0.0078 0.0078

0.2978 0.3045 0.3113 0.3182 0.3253 0.3324 0.3395 0.3468 0.3541 0.3615 0.3689 0.3763 0.3839 0.3915 0.3992 0.4070 0.4148 0.4226

0.0105 0.0114 0.0122 0.0130 0.0139 0.0147 0.0156 0.0164 0.0173 0.0181 0.0189 0.0196 0.0203 0.0210 0.0216 0.0221 0.0226 0.0230

46.5448 50.1280 53.7958 57.5275 61.3002 65.0888 68.8669 72.6061 76.2773 79.8502 83.2944 86.5794 89.6752 92.5527 95.1842 97.5437 99.6077 101.3551

6 8 10 13 15 17 20 22 25 28 31 33 35 38 40 41 43 44

0.0078 0.0079 0.0079 0.0080 0.0080 0.0080 0.0081 0.0081 0.0082 0.0083 0.0084

0.4305 0.4384 0.4463 0.4543 0.4623 0.4703 0.4784 0.4866 0.4948 0.5031 0.5115

0.0233 0.0235 0.0237 0.0238 0.0237 0.0237 0.0235 0.0232 0.0229 0.0225 0.0220

102.7678 103.8311 104.5339 104.8686 104.8318 104.4238 103.6489 102.5154 101.0351 99.2235 97.0993

45 46 46 46 46 45 44 43 41 40 37

0.0085 0.0087 0.0087 0.0087 0.0087 0.0089 0.0090 0.0093 0.0093 0.0094 0.0095

0.5200 0.5287 0.5374 0.5460 0.5548 0.5637 0.5727 0.5819 0.5912 0.6006 0.6101

0.0215 0.0208 0.0202 0.0195 0.0187 0.0179 0.0171 0.0163 0.0154 0.0146 0.0137

94.6839 92.0016 89.0786 85.9430 82.6241 79.1520 75.5572 71.8702 68.1210 64.3386 60.5510

34 31 29 26 24 20 17 13 11 8 6

0.0095 0.0096 0.0097

0.6196 0.6292 0.6389

0.0129 0.0120 0.0112

56.7846 53.0638 49.4112

4 2 1

0.0097 0.0098 0.0100 0.0100 0.0103 0.0106 0.0106 0.0107 0.0107 0.0108 0.0109 0.0110 0.0110 0.0112 0.0115 0.0115 0.0118 0.0120

0.6486 0.6584 0.6684 0.6784 0.6887 0.6993 0.7099 0.7206 0.7313 0.7421 0.7531 0.7641 0.7751 0.7863 0.7978 0.8094 0.8212 0.8332

0.0104 0.0096 0.0088 0.0081 0.0074 0.0068 0.0062 0.0056 0.0050 0.0045 0.0040 0.0036 0.0032 0.0028 0.0025 0.0022 0.0019 0.0017

45.8470 42.3893 39.0535 35.8527 32.7977 29.8968 27.1559 24.5789 22.1677 19.9222 17.8407 15.9201 14.1560 12.5427 11.0740 9.7426 8.5409 7.4609

0 0 1 2 5 9 14 21 29 39 52 67 85 109 142 174 224 276

0.0120 0.0121 0.0124 0.0129 0.0129 0.0137 0.0139 0.0143 0.0143 0.0151 0.0154

0.8452 0.8573 0.8697 0.8826 0.8955 0.9092 0.9231 0.9374 0.9517 0.9669 0.9823

0.0015 0.0013 0.0011 0.0009 0.0008 0.0007 0.0006 0.0005 0.0004 0.0004 0.0003

6.4944 5.6331 4.8687 4.1931 3.5985 3.0772 2.6222 2.2265 1.8838 1.5882 1.3343

335 407 509 659 797 1064 1325 1664 1994 2678 3330

0.0177

1.0000

0.0003

1.1170

5325

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Actividad 5 - Generación Manual de Variables Aleatorias

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