Simulacion Promodel Ejercicios Unidad 3

1. Utilice la prueba Chi-Cuadrada para determinar, con un nivel de confianza de 90%,

qué tipo de distribución siguen los datos. 0.022 0.119 0.154 0.202 0.433 0.569 0.818 0.843 0.877 1.182 1.264 1.29 1.392 1.395 1.422 1.453 1.486 1.495 1.53 1.578 1.611 1.781 1.816 2.007 2.052 2.072 2.103 2.155 2.333 2.381 2.44 2.498 2.547 2.63 2.637 2.717 2.945 3.032 3.043 3.078 3.151 3.28 3.384

1 2 3 4 5 6 7 8 9 10

i 0-2 2. -4 4.-6 6. -8 8. -10 10. - 12 12. -14 14 -16 16 -18 18- 20

Oi 23 26 17 14 6 5 3 2 3 1 100

Ei 10 10 10 10 10 10 10 10 10 10 100

((Ei-Oi)^2)/Ei 16.9 25.6 4.9 1.6 1.6 2.5 4.9 6.4 4.9 8.1 77.4

Viendo en tablas Conclusion como: 77.4<16.9 no se aceptan los ri como uniformes

Distribucion Lognormal

3.461 3.528 3.69 3.708 3.791 3.957 4.078 4.214 4.301 4.313 4.661 4.714 4.767 4.772 4.793 4.891 5.244 5.285 5.3 5.901 5.924 5.959 5.977 6.001 6.412 6.443 6.72 6.966 7.088 7.094 7.281 7.378 7.489 7.552 7.728 7.766 7.822 8.11 8.115 8.121 8.281 8.477 9.269 10.177 10.369 10.451 10.87

11.094 12.171 12.877 13.602 14.344 15.733 16.677 17.066 17.392 19.867

%,

2. A partir de la prueba Chi-cuadrada determine, con un nivel de confianza de 90%, qué tipo de distribución siguen los datos.

9.69 11.266 11.528 12.612 12.901 13.03 13.238 13.55 13.764 13.914 14.223 14.513 14.881 14.889 15.195 15.537 15.653 15.781 15.892 16.089 16.241 16.307 16.356 16.611 16.64 16.715 16.905 17.054 17.239 17.38 17.386 17.454 17.728 17.905 17.947 18.187 18.284 18.384 18.475 18.519 18.538

1 2 3 4 5 6 7 8 9 10

i 0-3 3. -6 6.-9 9. -12 12. -15 15. - 18 18 -21 21 -24 24 -27 27- 30

Oi 0 0 0 3 11 20 27 21 11 6 99

Ei 10 10 10 10 10 10 10 10 10 10 100

((Ei-Oi)^2)/Ei 10 10 10 4.9 0.1 10 28.9 12.1 0.1 1.6 87.7

Viendo en tablas Conclusion como: 87.7<16.9 no se aceptan los ri como uniformes


18.548 18.692 18.709 18.755 18.799 19.036 19.063 19.255 19.659 19.662 19.87 19.898 20.008 20.112 20.289 20.452 20.526 20.539 20.555 20.854 20.977 21.291 21.777 21.815 21.867 21.949 22.156 22.231 22.383 22.472 22.554 22.701 22.776 22.845 23.03 23.031 23.313 23.319 23.448 23.463 23.498 23.609 24.38 24.445 24.793 24.953 25.106

25.216 25.371 25.775 25.791 26.646 26.933 27.539 27.676 27.889 28.778 28.823 29.503

omo uniformes

3. Determine, con un nivel de confianza de 90%, qué tipo de distribución siguen los

datos utilice la prueba Chi-Cuadrada.

9.526 9.695 9.766 10.118 10.412 10.441 10.452 10.475 10.522 10.634 10.653 10.671 10.771 10.883 10.893 10.902 10.999 11.002 11.019 11.052 11.148 11.252 11.264 11.309 11.346 11.363 11.369 11.381 11.399 11.61 11.617 11.65 11.654 11.664 11.665 11.689 11.728 11.743 11.765 11.769 11.792 11.793

1 2 3 4 5 6 7 8 9 10

i 0-2 2. -4 4.-6 6. -8 8. -10 10. - 12 12. -14 14 -16 16 -18 18- 20

Oi 0 0 0 0 3 51 42 4 0 0 100

Ei 10 10 10 10 10 10 10 10 10 10 100

((Ei-Oi)^2)/Ei 10 10 10 10 4.9 168.1 102.4 3.6 10 10 339

Viendo en tablas Conclusion como: 339<16.9 no se aceptan los ri como uniformes


11.836 11.843 11.845 11.854 11.855 11.866 11.873 11.931 11.931 11.936 11.985 11.991 12.038 12.074 12.131 12.146 12.157 12.161 12.204 12.212 12.247 12.273 12.286 12.299 12.316 12.347 12.357 12.363 12.437 12.48 12.503 12.533 12.548 12.556 12.566 12.571 12.656 12.659 12.66 12.683 12.763 12.809 12.863 12.957 13.013 13.049 13.172

13.271 13.317 13.577 13.598 13.61 13.83 13.94 14.086 14.116 14.121 14.374

4. Emplee la prueba Chi-Cuadrada para determinar, con un nivel de confianza de 95%, qué tipo de distribución siguen los datos. Compruebe con la herramienta Stat::Fit de ProModel.

0.003 0.046 0.081 0.121 0.123 0.151 0.156 0.161 0.223 0.234 0.235 0.256 0.28 0.347 0.355 0.382 0.412 0.464 0.468 0.486 0.494 0.504 0.504 0.518 0.531 0.561 0.585 0.598 0.635 0.654 0.667 0.684 0.699 0.754 0.754 0.761 0.776 0.831 0.904 0.922 0.951 1.019

1 2 3 4 5 6 7 8 9 10

i 0-1 1 - 2. 2. - 3 3. - 4 4. - 5 5. - 6 6. - 7 7. - 8 8. - 9 9. - 10

Oi 41 26 20 6 2 1 1 2 1 0 100

Ei 10 10 10 10 10 10 10 10 10 10 100



1.182 1.182 1.187 1.202 1.228 1.229 1.243 1.337 1.38 1.383 1.419 1.424 1.427 1.45 1.458 1.506 1.525 1.597 1.613 1.639 1.662 1.679 1.78 1.876 1.962 2.06 2.087 2.198 2.258 2.294 2.312 2.327 2.393 2.451 2.516 2.606 2.628 2.66 2.7 2.756 2.771 2.775 2.815 2.898 2.933 3.141 3.192

3.258 3.399 3.582 3.591 4.518 4.923 5.715 6.985 7.145 7.66 8.055

de 95%, qué tipo de

((Ei-Oi)^2)/Ei 96.1 25.6 10 1.6 6.4 8.1 8.1 6.4 8.1 10 180.4

endo en tablas

e aceptan los ri como uniformes

5. Determine, con un nivel de confianza de 95%, qué tipo de distribución siguen los dígitos; emplee la prueba de Kolmogorov-Smirnov.

0.189 0.891 1.313 1.368 1.544 1.669 1.784 1.992 2.005 2.5 2.549 2.695 2.831 3.14 3.178 3.186 3.372 3.643 3.706 3.724 3.775 3.779 4.057 4.367 4.449 4.594 4.688 4.688 5.078 5.271 5.542 5.599 6.265 6.62 6.645 6.934 7.058 7.103 7.16 7.419 7.422

1 2 3 4 5 6 7 8 9 10

i 0-3 3 - 6. 6. - 9 9. - 12 12. - 15 15. - 18 18 - 21 21 - 24 24 - 27 27 - 30

13

Oi

0

Ei 10 10 10 10 10 10 10 10 10 10 100

((Ei-Oi)^2)/Ei 10 10 10 10 10 10 10 10 10 10 100



19

13 19 18 18 9 13 6 1 3

7.508 7.603 7.805 7.844 8.185 8.231 8.322 8.423 8.936 9.049 9.051 9.579 10.165 10.212 10.257 10.317 10.335 10.663 10.745 10.784 10.962 11.118 11.143 11.157 11.475 11.555 11.963 12.082 12.299 12.561 12.831 13.234 13.26 13.528 14.405 14.624 15.154 15.33 15.334 15.497 15.584 15.696 16.143 16.256 16.432 16.675 16.877

18

18

9

17.583 17.901 18.993 19.171 19.204 20.599 21.127 21.5 24.93 25.998 27.334 31.066

13

6 1

3

6, Determine, con un nivel de confianza de 90%, qué tipo de distribución siguen l emplee la prueba de Kolmogorov-Smirnov. Compruebe con la herramienta Stat::

Media= 18.9699 Varianza = 0.2863

i 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

Ri 9.784 10.279 12.858 15.907 16.032 16.452 16.463 16.677 16.713 16.939 17.487 17.532 17.926 18.436 18.515 18.825 19.209 19.301 19.364 20.169 20.346 21.073 21.878 22.029 22.208 23.479 23.787 24.076 26.853 28.501

i/n 0.0333 0.0667 0.1000 0.1333 0.1667 0.2000 0.2333 0.2667 0.3000 0.3333 0.3667 0.4000 0.4333 0.4667 0.5000 0.5333 0.5667 0.6000 0.6333 0.6667 0.7000 0.7333 0.7667 0.8000 0.8333 0.8667 0.9000 0.9333 0.9667 1.0000

i-1/n 0.0000 0.0333 0.0667 0.1000 0.1333 0.1667 0.2000 0.2333 0.2667 0.3000 0.3333 0.3667 0.4000 0.4333 0.4667 0.5000 0.5333 0.5667 0.6000 0.6333 0.6667 0.7000 0.7333 0.7667 0.8000 0.8333 0.8667 0.9000 0.9333 0.9667

17.574 18.338 2.69 21.427 15.305 21.151 14.24 18.739 22.658 24.477

16.257 23.217 20.232 14.581 21.17 14.817 24.154 14.206 22.24 17.673

(i/n)-ri -9.7507 -10.2123 -12.7580 -15.7737 -15.8653 -16.2520 -16.2297 -16.4103 -16.4130 -16.6057 -17.1203 -17.1320 -17.4927 -17.9693 -18.0150 -18.2917 -18.6423 -18.7010 -18.7307 -19.5023 -19.6460 -20.3397 -21.1113 -21.2290 -21.3747 -22.6123 -22.8870 -23.1427 -25.8863 -27.5010

ri-(i-1/n) 9.7840 10.2457 12.7913 15.8070 15.8987 16.2853 16.2630 16.4437 16.4463 16.6390 17.1537 17.1653 17.5260 18.0027 18.0483 18.3250 18.6757 18.7343 18.7640 19.5357 19.6793 20.3730 21.1447 21.2623 21.4080 22.6457 22.9203 23.1760 25.9197 27.5343

13.345 15.495 21.411 23.523 16.155 14.702 19.501 17.471 19.916 22.422 D+

22.863 17.403 21.107 19.87 22.88 27.014 16.238 18.59 16.537 13.373 D-

-9.7507

27.5343

En tablas 0.220 Como 0.22<27.5343 se aceptan los numeros

Los datos siguen una distr

de distribución siguen los datos; on la herramienta Stat::Fit de ProModel. 12.846 22.671 14.238 16.021 20.774 12.165 20.795 18.587 23.96 21.971 D

27.5343

15.557 17.469 20.098 18.107 14.255 16.597 25.924 19.929 14.417 20.549

16.526 18.489 19.881 13.315 12.478 21.404 18.874 25.354 18.338 24.509

n los numeros

os datos siguen una distribucion lognormal y uniforme

7. Determine, con un nivel de confianza de 90%, qué tipo de distribución

siguen los datos usando la prueba de Kolmogorov-Smirnov, Compruebe con Stat::Fit.

i 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

Ri 4.548 3.242 6.303 5.225 5.307 6.536 4.769 3.154 5.427 3.404 5.366 5.919 8.503 4.743 6.093 3.822 2.938 6.316 6.532 2.917 3.136 4.705 6.476 5.966 8.546 8.441 4.484 3.546

i/n 0.0333 0.0667 0.1000 0.1333 0.1667 0.2000 0.2333 0.2667 0.3000 0.3333 0.3667 0.4000 0.4333 0.4667 0.5000 0.5333 0.5667 0.6000 0.6333 0.6667 0.7000 0.7333 0.7667 0.8000 0.8333 0.8667 0.9000 0.9333

1.979 5.53 3.863 7.228 4.72 6.176 6.459 4.364 6.101 6.739

6.097 6.891 1.738 6.03 5.771 5.059 3.083 8.986 2.625 7.049

3.823 5.997 2.913 6.184 4.521 5.325 6.199 4.195 4.463 5.743

i-1/n 0.0000 0.0333 0.0667 0.1000 0.1333 0.1667 0.2000 0.2333 0.2667 0.3000 0.3333 0.3667 0.4000 0.4333 0.4667 0.5000 0.5333 0.5667 0.6000 0.6333 0.6667 0.7000 0.7333 0.7667 0.8000 0.8333 0.8667 0.9000

(i/n)-ri -4.5147 -3.1753 -6.2030 -5.0917 -5.1403 -6.3360 -4.5357 -2.8873 -5.1270 -3.0707 -4.9993 -5.5190 -8.0697 -4.2763 -5.5930 -3.2887 -2.3713 -5.7160 -5.8987 -2.2503 -2.4360 -3.9717 -5.7093 -5.1660 -7.7127 -7.5743 -3.5840 -2.6127

ri-(i-1/n) 4.5480 3.2087 6.2363 5.1250 5.1737 6.3693 4.5690 2.9207 5.1603 3.1040 5.0327 5.5523 8.1030 4.3097 5.6263 3.3220 2.4047 5.7493 5.9320 2.2837 2.4693 4.0050 5.7427 5.1993 7.7460 7.6077 3.6173 2.6460

5.52 6.64 5.171 7.6 3.715 6.478 2.59 2.952 7.9 5.448

D+

4.203 6.376 6.856 5.716 5.368 4.229 7.407 3.59 3.715 3.958

D-

-2.2503

7.746

29 30

3.431 5.769

0.9667 1.0000

0.9333 0.9667

-2.4643 -4.7690

2.4977 4.8023


Los datos siguen una distribucion lognorm

4.972 6.86 5.665 5.781 1.871 5.619 7.001 7.356 4.881 6.632

D

8.429 5.991 3.396 4.465 1.629 4.062 8.501 6.269 7.41 7.036

n una distribucion lognormal y exponencial

8. Utilice la prueba de Anderson-Darling para determinar, con un nivel de confianza de 90% qué tipo de distribución siguen los datos. Compruebe con Stai::Fit.

-1.413 -0.618 1.542 -1.152 -0.93 -0.418 1.567 0.913 0.01 1.077

i 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

Yi 0.889 -1.553 -0.204 0.436 1.672 -1.638 0.431 0.564 1.24 1.219 -0.056 1.51 -2.067 -0.869 -1.293 -1.018 -1.322 2.295 -1.108 0.095 1.583 0.824 1.905 -0.112 -0.559 -0.289 1.97 2.21 0.683 -0.354

Y 50+1-i -1.525 -1.691 -2.477 -3.541 -5.343 -4.12 -5.983 -7.965 -7.373 -7.528 -11.631 -11.104 -12.281 -13.952 -14.296 -14.717 -15.635 -15.267 -18.86 -18.11 -20.354 -20.317 -19.79 -21.03 -24.289 -25.559 -26.112 -25.095 -27.176 -27.417

2*i-1 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59

PEA(Yi) 1-PEA(Y50+1-i) 0.143 0.0123 0.0332 0.0241 0.0433 0.0586 0.888 0.0786 0.089 0.0962 0.0978 0.1098 0.1174 0.111 0.1252 0.1227 0.1256 0.1484 0.1931 0.1707 0.2207 0.1787 0.232 0.184 0.2389 0.2887 0.2529 0.2943 0.2741 0.3012 0.2865 0.3021 0.314 0.3033 0.3205 0.3543 0.3214 0.3593 0.3756 0.3624 0.4029 0.3721 0.4203 0.4194 0.4392 0.4425 0.4514 0.4494 0.4871 0.4521 0.5479 0.5129 0.5506 0.5486 0.5575 0.5608 0.5806 0.5797 0.6279 0.5971

0.066 -1.425 0.27 0.512 0.121 1.317 -1.717 -0.697 -0.429 0.2

Ln (PEA(Yi)) -1.9449106 -3.4052054 -3.1396026 -0.1187835 -2.4191189 -2.3248307 -2.1421684 -2.0778428 -2.074653 -1.6445471 -1.510951 -1.4610179 -1.4317102 -1.3747611 -1.2942623 -1.2500167 -1.1583623 -1.137873 -1.1350688 -0.9792305 -0.9090669 -0.8667865 -0.8228004 -0.7954014 -0.7192858 -0.6016625 -0.5967467 -0.5842928 -0.5436932 -0.4653744

31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

0.89 -0.86 1.733 0.365 0.283 -0.296 -0.952 -0.281 -0.104 -1.631 1.472 0.627 -0.965 0.017 0.88 -1.343 -0.541 -0.477 -0.691 -1.525

-29.905 -32.108 -29.705 -34.322 -35.018 -36.293 -36.869 -39.067 -36.49 -39.056 -38.781 -39.76 -41.436 -42.569 -45.638 -43.328 -45.564 -47.204 -49.553 -48.111

61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99

0.6376 0.6407 0.6457 0.6967 0.6979 0.6988 0.7057 0.7113 0.816 0.8213 0.8293 0.8516 0.8773 0.889 0.8902 0.9038 0.9232 0.9414 0.9759 0.9877

0.6244 0.6786 0.6795 0.686 0.7135 0.7259 0.7471 0.7611 0.768 0.7793 0.8069 0.8744 0.8748 0.8826 0.9022 0.911 0.9112 0.9567 0.9668 0.9857

-0.4500442 -0.445194 -0.4374203 -0.3614004 -0.3596795 -0.3583907 -0.3485651 -0.340661 -0.2033409 -0.1968668 -0.1871733 -0.1606383 -0.1309063 -0.117658 -0.1163091 -0.1011472 -0.0799094 -0.0603872 -0.0243952 -0.0123763

Los datos siguen uns distribucion lognorm

nar, con un nivel de confianza de 90%, pruebe con Stai::Fit.

-0.423 0.061 2.293 2.324 0.595 0.249 0.125 -0.145 -1.42 -0.959

Ln(1-PEA(Y50+1-i)) -4.398156017 -3.725543438 -2.837020582 -2.54338358 -2.341325921 -2.20909475 -2.198225078 -2.098012927 -1.907843948 -1.767847649 -1.722046857 -1.692819521 -1.242367192 -1.223155624 -1.199980783 -1.196997191 -1.193032864 -1.037611267 -1.023597585 -1.015006705 -0.988592644 -0.868930161 -0.815314815 -0.799841919 -0.793851885 -0.667674385 -0.6003857 -0.578390943 -0.545244551 -0.515670675

-0.174 0.7 -0.889 0.654 0.597 0.937 -0.608 -1.088 -0.07 -0.144

(2*i-1)*(Ln(PEA(Yi))+ Ln(1-PEA(Y50+1-i)))i))) -6.343066665 -21.39224652 -29.88311613 -18.63516981 -42.84400348 -49.87317997 -56.42511484 -62.63783621 -67.70244854 -64.83550004 -67.89295427 -72.53826086 -66.85193542 -70.14375222 -72.3330487 -75.85743194 -77.59604019 -76.14194944 -79.87065719 -77.77525222 -77.80404075 -74.63581799 -73.71518415 -74.97643669 -74.14374842 -64.73618063 -63.4480165 -63.94760454 -62.06945335 -57.88165714

-1.139 -0.078 0.099 -1.281 -0.185 -0.67 1.027 0.137 1.517 -1.169

-0.47096409 -0.387723427 -0.386398045 -0.376877651 -0.337572842 -0.320343015 -0.291556234 -0.272990524 -0.263965546 -0.249359198 -0.214555534 -0.134217342 -0.13375999 -0.124883182 -0.102919054 -0.093212382 -0.092992867 -0.044265416 -0.03376363 -0.01440323

-56.18150275 -52.47379475 -53.54819111 -49.46462789 -48.11040836 -48.19009379 -46.72885453 -46.02386407 -35.98259818 -35.25185608 -32.54003617 -24.47302211 -22.4966321 -21.10108663 -19.5113077 -17.6867203 -16.07990926 -9.9419938 -5.641402338 -2.651170637

os datos siguen uns distribucion lognormal y una distribucion uniforme

9. Determine, con un nivel de confianza de 90%r qué tipo de distribución siguen los da-tos; utilice la prueba de Kolmogorov-Smirnov.

i 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

Ri 7.982 18.951 6.361 3.382 37.134 17.684 6.839 3.274 22.836 12.427 40.122 12.348 6.405 14.387 21.099 8.814 7.073 7.325 14.432 11.811 5.862 8.725 34.45 10.037 9.021 22.939 10.708 10.046 14.65

i/n 0.0333 0.0667 0.1000 0.1333 0.1667 0.2000 0.2333 0.2667 0.3000 0.3333 0.3667 0.4000 0.4333 0.4667 0.5000 0.5333 0.5667 0.6000 0.6333 0.6667 0.7000 0.7333 0.7667 0.8000 0.8333 0.8667 0.9000 0.9333 0.9667

21.92 11.536 24.956 5.481 6.08 2.491 25.237 9.888 2.898 6.848

7.902 10.187 5.442 2.959 9.053 10.123 7.588 13.798 20.041 7.197

10.824 11.442 12.996 7.503 5.178 3.244 1.152 15.255 10.228 12.156

i-1/n 0.0000 0.0333 0.0667 0.1000 0.1333 0.1667 0.2000 0.2333 0.2667 0.3000 0.3333 0.3667 0.4000 0.4333 0.4667 0.5000 0.5333 0.5667 0.6000 0.6333 0.6667 0.7000 0.7333 0.7667 0.8000 0.8333 0.8667 0.9000 0.9333

(i/n)-ri -7.9487 -18.8843 -6.2610 -3.2487 -36.9673 -17.4840 -6.6057 -3.0073 -22.5360 -12.0937 -39.7553 -11.9480 -5.9717 -13.9203 -20.5990 -8.2807 -6.5063 -6.7250 -13.7987 -11.1443 -5.1620 -7.9917 -33.6833 -9.2370 -8.1877 -22.0723 -9.8080 -9.1127 -13.6833

ri-(i-1/n) 7.9820 18.9177 6.2943 3.2820 37.0007 17.5173 6.6390 3.0407 22.5693 12.1270 39.7887 11.9813 6.0050 13.9537 20.6323 8.3140 6.5397 6.7583 13.8320 11.1777 5.1953 8.0250 33.7167 9.2703 8.2210 22.1057 9.8413 9.1460 13.7167

22.258 13.396 5.073 4.159 18.7 9.433 8.059 20.507 9.553 1.674

D+

13.343 13.07 13.62 23.466 9.056 11.774 26.399 11.147 19.87 8.582

D-

-3.0073

39.7887

30

24.699

1.0000

0.9667

-23.6990

23.7323


11.045 13.668 11.02 5.219 6.647 3.271 29.285 19.691 8.52 16.293

D

39.7887

23.603 7.954 11.729 11.713 5.767 10.39 22.35 7.711 26.182 16.126

10. A partir de la prueba de Kolmogorov-Smirnov, determine con un nivel de confianza de 90% qué tipo de distribución siguen los datos.

i 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

Ri 5.091 6.752 11.584 9.595 7.558 4.179 13.47 9.71 14.135 12.436 11.319 10.64 13.333 13.784 8.12 10.035 1.512 5.259 5.937 8.153 3.274 7.242 10.081 4.867 6.451 5.599 11.317 8.086 2.954 5.418

i/n 0.0333 0.0667 0.1000 0.1333 0.1667 0.2000 0.2333 0.2667 0.3000 0.3333 0.3667 0.4000 0.4333 0.4667 0.5000 0.5333 0.5667 0.6000 0.6333 0.6667 0.7000 0.7333 0.7667 0.8000 0.8333 0.8667 0.9000 0.9333 0.9667 1.0000

3.366 2.91 11.892 3.171 10.263 5.582 9.799 4.141 9.264 4.028

12.233 8.391 14.542 7.782 5.367 4.836 7.825 2.972 14.575 6.515

5.725 2.288 9.851 5.682 3.059 8.663 9.464 14.575 6.742 9.474

i-1/n 0.0000 0.0333 0.0667 0.1000 0.1333 0.1667 0.2000 0.2333 0.2667 0.3000 0.3333 0.3667 0.4000 0.4333 0.4667 0.5000 0.5333 0.5667 0.6000 0.6333 0.6667 0.7000 0.7333 0.7667 0.8000 0.8333 0.8667 0.9000 0.9333 0.9667

(i/n)-ri -5.0577 -6.6853 -11.4840 -9.4617 -7.3913 -3.9790 -13.2367 -9.4433 -13.8350 -12.1027 -10.9523 -10.2400 -12.8997 -13.3173 -7.6200 -9.5017 -0.9453 -4.6590 -5.3037 -7.4863 -2.5740 -6.5087 -9.3143 -4.0670 -5.6177 -4.7323 -10.4170 -7.1527 -1.9873 -4.4180

ri-(i-1/n) 5.0910 6.7187 11.5173 9.4950 7.4247 4.0123 13.2700 9.4767 13.8683 12.1360 10.9857 10.2733 12.9330 13.3507 7.6533 9.5350 0.9787 4.6923 5.3370 7.5197 2.6073 6.5420 9.3477 4.1003 5.6510 4.7657 10.4503 7.1860 2.0207 4.4513

9.186 4.582 11.088 9.587 6.341 6.975 7.799 2.248 5.551 6.817

D+

8.232 6.114 6.301 12.519 3.613 8.441 6.929 6.565 5.313 10.19

D-

13.8683

-0.9453



nivel de confianza

6.545 9.965 5.35 9.964 3.068 2.064 8.915 13.418 6.348 4.961

D

13.8683

6.481 10.643 3.465 1.298 7.291 5.147 8.007 5.238 5.723 13.263

11. Determine, con un nivel de confianza de 90%, qué tipo de distribución siguen los datos; utilice la prueba de Kolmogorov-Smirnov.

i 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

Ri 1.338 1.198 1.852 3.05 1.003 0.286 2.283 0.388 0.095 0.265 0.58 0.294 1.586 4.117 1.645 0.395 0.483 2.156 1.355 7.487 0.53 0.049 1.426 4.688 0.46 1.581 0.774 0.429 2.267 2.032

0.102 3.661 0.664 2.342 2.35 3.986 0.852 4.276 2.859 2.852

0.285 3.072 6.032 2.954 3.983 2.416 4.342 0.371 0.799 0.04

0.725 5.193 0.093 0.883 1.517 0.577 0.064 4.52 4.718 1.86

5.567 0.329 3.856 1.79 0.695 0.617 0.299 0.408 8.664 0.716

i/n 0.0333 0.0667 0.1000 0.1333 0.1667 0.2000 0.2333 0.2667 0.3000 0.3333 0.3667 0.4000 0.4333 0.4667 0.5000 0.5333 0.5667 0.6000 0.6333 0.6667 0.7000 0.7333 0.7667 0.8000 0.8333 0.8667 0.9000 0.9333 0.9667 1.0000

i-1/n 0.0000 0.0333 0.0667 0.1000 0.1333 0.1667 0.2000 0.2333 0.2667 0.3000 0.3333 0.3667 0.4000 0.4333 0.4667 0.5000 0.5333 0.5667 0.6000 0.6333 0.6667 0.7000 0.7333 0.7667 0.8000 0.8333 0.8667 0.9000 0.9333 0.9667

(i/n)-ri 0.3380 -0.8020 -1.1480 -0.9500 -3.9970 -5.7140 -4.7170 -7.6120 -8.9050 -9.7350 -10.4200 -11.7060 -11.4140 -9.8830 -13.3550 -15.6050 -16.5170 -15.8440 -17.6450 -12.5130 -20.4700 -21.9510 -21.5740 -19.3120 -24.5400 -24.4190 -26.2260 -27.5710 -26.7330 -27.9680

ri-(i-1/n) 0.9667 1.9333 2.9000 3.8667 4.8333 5.8000 6.7667 7.7333 8.7000 9.6667 10.6333 11.6000 12.5667 13.5333 14.5000 15.4667 16.4333 17.4000 18.3667 19.3333 20.3000 21.2667 22.2333 23.2000 24.1667 25.1333 26.1000 27.0667 28.0333 29.0000

6.773 2.721 1.779 3.847 3.564 1.494 0.214 0.113 0.339 3.551

D+

0.3380

En tablas 0.220 Como 0.22<29 se aceptan los numeros


0.101 0.988 1.729 2.659 0.573 0.468 3.294 0.24 1.892 0.493

D-

5.549 0.716 1.456 3.622 0.204 1.037 0.345 2.923 1.262 0.269

D

29

12. Determine, con un nivel de confianza de 95%, qué Tipo de distribución siguen los da-tos;

emplee la prueba de Kolmogorov-Smirnov. Compruebe con Stat :Fit. 18.39 24.364 22.105 15.625 19.743 25.275 22.189 29.122 24.007 24.985

i 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

Ri 26.739 23.396 21.326 17.539 26.421 20.931 28.013 25.57 22.518 29.791 22.607 28.553 15.138 19.921 18.044 18.562 26693 18.746 18.883 17.89 19.584 24.449 21.15 22.216 25.744 26.714 29.751 16.818 26.128 15.515

i/n 0.0333 0.0667 0.1000 0.1333 0.1667 0.2000 0.2333 0.2667 0.3000 0.3333 0.3667 0.4000 0.4333 0.4667 0.5000 0.5333 0.5667 0.6000 0.6333 0.6667 0.7000 0.7333 0.7667 0.8000 0.8333 0.8667 0.9000 0.9333 0.9667 1.0000

19.825 19.2 25.105 16.168 24.525 24.56 20.807 27.19 28.127 17.717

23.279 21.265 22.137 29.769 18.112 22.09 27.339 26.915 25.213 19.063

i-1/n (i/n)-ri ri-(i-1/n) 0.0000 -26.7057 26.7390 0.0333 -23.3293 23.3627 0.0667 -21.2260 21.2593 0.1000 -17.4057 17.4390 0.1333 -26.2543 26.2877 0.1667 -20.7310 20.7643 0.2000 -27.7797 27.8130 0.2333 -25.3033 25.3367 0.2667 -22.2180 22.2513 0.3000 -29.4577 29.4910 0.3333 -22.2403 22.2737 0.3667 -28.1530 28.1863 0.4000 -14.7047 14.7380 0.4333 -19.4543 19.4877 0.4667 -17.5440 17.5773 0.5000 -18.0287 18.0620 0.5333 -26692.4333 26692.4667 0.5667 -18.1460 18.1793 0.6000 -18.2497 18.2830 0.6333 -17.2233 17.2567 0.6667 -18.8840 18.9173 0.7000 -23.7157 23.7490 0.7333 -20.3833 20.4167 0.7667 -21.4160 21.4493 0.8000 -24.9107 24.9440 0.8333 -25.8473 25.8807 0.8667 -28.8510 28.8843 0.9000 -15.8847 15.9180 0.9333 -25.1613 25.1947 0.9667 -14.5150 14.5483

23.206 16.905 27.514 18.158 26.259 19.608 22.556 26.844 19.964 29.986

D+

19.351 27.313 15.766 18.293 19.466 15.447 24.059 19.573 27.141 24.074

D-

29.491

-14.515

En tablas 0.240 Como 0.24>-14.515 No se aceptan los numeros

15.24 18.097 22.029 15.858 26.276 29.631 15.724 26.853 25.458 23.517

D

29.491

15.792 20.233 25.164 25.111 25.948 28.821 21.614 17.053 26.06 20.733

Los datos no siguen ninguna distribucion

13. Determine, don un nivel de confianza de 90%, qué tipo de distribución liguen los datos usando la prueba de Anderson-Darling. Compruebe con Stat :Fit

7.717 6.377 6.15 6.174 7.814 7.354 7.99 7.495 5.021 6.351

i 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

7.971 6.155 5.983 5.962 6.238 5.826 5.793 6.004 6.8 6.438

Yi 5.021 5.057 5.245 5.261 5.316 5.547 5.549 5.741 5.793 5.826 5.858 5.962 5.983 5.994 6.004 6.061 6.15 6.15 6.153 6.155 6.174 6.238 6.246 6.351 6.377 6.438

5.261 7.512 6.061 6.153 7.484 5.858 5.057 7.374 7.322 7.76

Y50+1-i 7.99 6.99 5.99 4.99 3.99 2.99 1.99 0.99 -0.01 -1.01 -2.01 -3.01 -4.01 -5.01 -6.01 -7.01 -8.01 -9.01 -10.01 -11.01 -12.01 -13.01 -14.01 -15.01 -16.01 -17.01

5.994 7.936 7.492 6.838 6.15 5.316 5.245 7.071 7.84 7.771

2*i-1 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

7.215 7.96 6.974 5.741 7.561 7.081 6.246 5.549 5.547 7.118

PEA(Yi) 0.143 0.0332 0.0433 0.888 0.089 0.0978 0.1174 0.1252 0.1256 0.1931 0.2207 0.232 0.2389 0.2529 0.2741 0.2865 0.314 0.3205 0.3214 0.3756 0.4029 0.4203 0.4392 0.4514 0.4871 0.5479

6.1 6.157 5.386 5.478 7.734 6.476 7.538 6.932 5.601 5.5

1-PEA(Y50+1-i) 0.0123 0.0241 0.0586 0.0786 0.0962 0.1098 0.111 0.1227 0.1484 0.1707 0.1787 0.184 0.2887 0.2943 0.3012 0.3021 0.3033 0.3543 0.3593 0.3624 0.3721 0.4194 0.4425 0.4494 0.4521 0.5129

6.876 5.796 6.347 5.471 5.595 7.394 7.314 6.262 6.524 5.901

Ln (PEA(Yi)) -1.9449 -3.4052 -3.1396 -0.1188 -2.4191 -2.3248 -2.1422 -2.0778 -2.0747 -1.6445 -1.5110 -1.4610 -1.4317 -1.3748 -1.2943 -1.2500 -1.1584 -1.1379 -1.1351 -0.9792 -0.9091 -0.8668 -0.8228 -0.7954 -0.7193 -0.6017

27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

6.8 6.838 6.974 7.071 7.081 7.118 7.215 7.322 7.354 7.374 7.484 7.492 7.495 7.512 7.561 7.717 7.76 7.771 7.814 7.84 7.936 7.96 7.971 7.99

-18.01 -19.01 -20.01 -21.01 -22.01 -23.01 -24.01 -25.01 -26.01 -27.01 -28.01 -29.01 -30.01 -31.01 -32.01 -33.01 -34.01 -35.01 -36.01 -37.01 -38.01 -39.01 -40.01 -41.01

53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99

0.5506 0.5575 0.5806 0.6279 0.6376 0.6407 0.6457 0.6967 0.6979 0.6988 0.7057 0.7113 0.816 0.8213 0.8293 0.8516 0.8773 0.889 0.8902 0.9038 0.9232 0.9414 0.9759 0.9877

0.5486 0.5608 0.5797 0.5971 0.6244 0.6786 0.6795 0.686 0.7135 0.7259 0.7471 0.7611 0.768 0.7793 0.8069 0.8744 0.8748 0.8826 0.9022 0.911 0.9112 0.9567 0.9668 0.9857

-0.5967 -0.5843 -0.5437 -0.4654 -0.4500 -0.4452 -0.4374 -0.3614 -0.3597 -0.3584 -0.3486 -0.3407 -0.2033 -0.1969 -0.1872 -0.1606 -0.1309 -0.1177 -0.1163 -0.1011 -0.0799 -0.0604 -0.0244 -0.0124

Los datos siguen una distribucion uniforme

7.514 7.579 5.053 7.745 7.587 5.304 5.909 5.531 6.169 5.104

Ln(1-PEA(Y50+1-i)) -4.3982 -3.7255 -2.8370 -2.5434 -2.3413 -2.2091 -2.1982 -2.0980 -1.9078 -1.7678 -1.7220 -1.6928 -1.2424 -1.2232 -1.2000 -1.1970 -1.1930 -1.0376 -1.0236 -1.0150 -0.9886 -0.8689 -0.8153 -0.7998 -0.7939 -0.6677

6.409 6.45 5.129 5.057 5.235 5.175 6.215 6.335 5.484 7.633

(2*i-1)*(Ln(PEA(Yi))+ Ln(1-PEA(Y50+1-i)))i))) -1.9326 -10.1433 -15.4050 -0.2813 -20.9063 -24.3653 -26.4052 -29.3271 -32.7463 -28.0031 -27.9773 -29.3714 -28.5753 -29.1725 -28.7988 -29.3854 -28.2171 -27.4251 -28.7034 -24.0564 -22.0156 -19.2376 -17.1135 -16.2621 -13.0921 -4.5269

6.679 6.719 5.922 5.548 7.872 6.499 6.949 5.271 6.823 6.074

-0.6004 -0.5784 -0.5452 -0.5157 -0.4710 -0.3877 -0.3864 -0.3769 -0.3376 -0.3203 -0.2916 -0.2730 -0.2640 -0.2494 -0.2146 -0.1342 -0.1338 -0.1249 -0.1029 -0.0932 -0.0930 -0.0443 -0.0338 -0.0144

-2.5518 -1.2921 2.0524 7.7718 10.6357 14.7046 15.7352 21.7482 24.4136 26.0932 29.0931 31.5329 43.4787 46.0122 50.1979 59.2422 63.2310 66.5500 69.9443 73.6966 77.3100 85.1497 91.4133 96.3590

60.197 60.659 60.747 61.771 62.614 62.686 62.849 63.185 63.391 63.479 63.499 63.766 64.31 65.272 66.832 68.147 68.18 68.181 68.51 68.775 69.235 69.346 69.716 69.933 70.205 70.569 70.684 71.68 72.537 72.55 73.105 73.495 73.711 73.864 74.473 75.107 75.425 75.734 75.734 76.159 76.248 76.276 76.753 77.024 77.148 77.388 77.588

14. Utilice la prueba Chi-Cuadrada para determinar, con un nivel de confianza de 95%

qué tipo de distribución siguen los datos. Compruebe con Siat::Fit.

1 2 3 4 5 6 7 8 9 10

i 60-64 64-68 68-72 72-76 76-80 80-84 84-88 88-92 92-96 96-100

Oi 12 3 13 11 10 10 5 14 9 13 100

Ei 10 10 10 10 10 10 10 10 10 10 100

La distribucion que se siguen en estos datos es uniform

79.007 79.56 80.042 80.15 81.057 81.149 81.931 82.187 82.416 83.537 83.704 83.945 84.366 86.06 86.162 86.478 86.95 88.371 88.431 88.819 89.36 89.607 90.108 90.591 90.697 90.854 91.051 91.262 91.325 91.54 91.917 92.229 92.978 93.2 93.535 93.645 95.076 95.181 95.804 95.882 96.594 96.829 96.893 96.937 97.305 97.491 97.58

97.844 97.891 97.926 98.002 98.783 99.813

de confianza de 95%

((Ei-Oi)^2)/Ei 0.4 4.9 0.9 0.1 0 0 2.5 1.6 0.1 0.9 11.4

en estos datos es uniforme


datos Emplee Ia prueba Chi-Cuadrada y compruebe con Stat::Fit H0: Binomial H1: Otra Distribucion 1.316 1.34 i Oi Ei ((Ei-Oi)^2)/Ei 1.443 1 0-1 9 16.6 3.4795 1.556 2 1-2. 22 16.6 1.7566 1.677 3 2-3. 28 16.6 7.8289 1.689 4 3-4. 26 16.6 5.3229 1.806 5 4-5. 11 16.6 1.8892 1.81 6 5-6. 4 16.6 9.5639 1.874 100 99.6 29.8410 2.076 2.171 1.61 Viendo en tablas 2.173 2.225 Conclusion como: 29.84<1.61 no se aceptan los ri como uniformes 2.246 2.33 H0: 2.369 2.37

2.37 2.499 2.639 2.649 2.682 2.727 2.744 2.749 2.782 2.804 2.848 2.912 2.919 2.949 3.009 3.018 3.028 3.046 3.049 3.137 3.2 3.206 3.292

Distribucion Binomial

Intervalo 0-4 5 6 7 8.-9

No. de Observaciones Oi 10 9 14 7 10

p(x) 0.1521 0.2091 0.273 0.2292 0.1366

Ei=50*p(x) 7.605 10.455 13.65 11.46 6.83

Total

50

1

50

3.309 3.347 3.351 3.361 3.408 3.449 3.501 3.572 3.587 3.722 3.724 3.775 3.786 3.796 3.82 3.899 3.903 3.953 3.964 4.035 4.043 4.057 4.075 4.098 4.102 4.111 4.123 4.142 4.164 4.328 4.339 4.344 4.347 4.374 4.375 4.398 4.463 4.574 4.606 4.87 4.879 4.907 4.951 4.968 4.993 5.006 5.08

5.187 5.246 5.329 5.331 5.337 5.444 5.617 5.813 5.828 6.351 6.385 6.43 6.767

o uniformes

(Ei-Oi)2/Ei 0.7537 0.2023 0.009 1.7345 1.4698 4.1693

16. Determine, con un nivel de confianza de 90%, qué tipo de distribución siguen los da-tos;

utilice la prueba de Anderson-Darling. Compruebe con Stat;:Fit.

198.912 186.72 186.615 191.445 183.463 191.088 176.583 193.267 198.414 203.231

193.496 175.625 191.5 184.243 193.388 178.781 187.396 192.581 174.54 192.099

198.169 193.319 191.643 185.089 193.112 199.534 198.267 195.991 194.575 177.14

H0: Normal H1: Otra distribucion

i 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

Yi 172.582 172.773 173.618 174.54 175.524 175.625 176.583 176.613 177.14 178.781 179.564 179.576 180.002 180.174 180.861 181.175 181.183 181.189 182.241 183.386 183.463 183.73 184.097 184.243 184.283 184.548

186.553 208.652 201.017 194.686 194.638 191.382 181.183 200.364 184.283 172.582

186.699 180.861 187.908 188.845 184.73 173.618 186.406 188.597 194.842 188.939

189.485 189.234 180.002 194.979 188.484 193.244 192.473 188.87 186.476 183.386

197.916 179.564 192.118 203.149 194.847 185.665 193.006 191.077 196.176 180.174

H0: Los datos siguen la distribucion Normal

Y50+1-i 191.077 190.077 189.077 188.077 187.077 186.077 185.077 184.077 183.077 182.077 181.077 180.077 179.077 178.077 177.077 176.077 175.077 174.077 173.077 172.077 171.077 170.077 169.077 168.077 167.077 166.077

2*i-1 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

PEA(Yi) 0.143 0.0332 0.0433 0.888 0.089 0.0978 0.1174 0.1252 0.1256 0.1931 0.2207 0.232 0.2389 0.2529 0.2741 0.2865 0.314 0.3205 0.3214 0.3756 0.4029 0.4203 0.4392 0.4514 0.4871 0.5479

1-PEA(Y50+1-i) Ln (PEA(Yi)) 0.0123 -1.9449 0.0241 -3.4052 0.0586 -3.1396 0.0786 -0.1188 0.0962 -2.4191 0.1098 -2.3248 0.111 -2.1422 0.1227 -2.0778 0.1484 -2.0747 0.1707 -1.6445 0.1787 -1.5110 0.184 -1.4610 0.2887 -1.4317 0.2943 -1.3748 0.3012 -1.2943 0.3021 -1.2500 0.3033 -1.1584 0.3543 -1.1379 0.3593 -1.1351 0.3624 -0.9792 0.3721 -0.9091 0.4194 -0.8668 0.4425 -0.8228 0.4494 -0.7954 0.4521 -0.7193 0.5129 -0.6017

27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

184.73 185.089 185.665 185.913 186.406 186.476 186.553 186.615 186.699 186.72 187.396 187.85 187.908 188.484 188.597 188.845 188.87 188.939 189.234 189.485 189.795 190.21 190.292 191.077

165.077 164.077 163.077 162.077 161.077 160.077 159.077 158.077 157.077 156.077 155.077 154.077 153.077 152.077 151.077 150.077 149.077 148.077 147.077 146.077 145.077 144.077 143.077 142.077

53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99

0.5506 0.5575 0.5806 0.6279 0.6376 0.6407 0.6457 0.6967 0.6979 0.6988 0.7057 0.7113 0.816 0.8213 0.8293 0.8516 0.8773 0.889 0.8902 0.9038 0.9232 0.9414 0.9759 0.9877

0.5486 0.5608 0.5797 0.5971 0.6244 0.6786 0.6795 0.686 0.7135 0.7259 0.7471 0.7611 0.768 0.7793 0.8069 0.8744 0.8748 0.8826 0.9022 0.911 0.9112 0.9567 0.9668 0.9857

-0.5967 -0.5843 -0.5437 -0.4654 -0.4500 -0.4452 -0.4374 -0.3614 -0.3597 -0.3584 -0.3486 -0.3407 -0.2033 -0.1969 -0.1872 -0.1606 -0.1309 -0.1177 -0.1163 -0.1011 -0.0799 -0.0604 -0.0244 -0.0124

184.548 200.401 200.353 202.014 199.871 192.927 192.881 206.708 183.73 195.355

176.613 206.452 197.755 179.576 172.773 175.524 182.241 190.292 197.7 193.626

(2*i-1)*(Ln(PEA(Yi))+ Ln(1-PEA(Y50+1-i)))i))) Ln(1-PEA(Y50+1-i)) -4.3982 -1.9326 -3.7255 -10.1433 -2.8370 -15.4050 -2.5434 -0.2813 -2.3413 -20.9063 -2.2091 -24.3653 -2.1982 -26.4052 -2.0980 -29.3271 -1.9078 -32.7463 -1.7678 -28.0031 -1.7220 -27.9773 -1.6928 -29.3714 -1.2424 -28.5753 -1.2232 -29.1725 -1.2000 -28.7988 -1.1970 -29.3854 -1.1930 -28.2171 -1.0376 -27.4251 -1.0236 -28.7034 -1.0150 -24.0564 -0.9886 -22.0156 -0.8689 -19.2376 -0.8153 -17.1135 -0.7998 -16.2621 -0.7939 -13.0921 -0.6677 -4.5269

194.656 185.913 190.21 181.175 181.189 189.795 187.85 198.489 184.097 206.255

-0.6004 -0.5784 -0.5452 -0.5157 -0.4710 -0.3877 -0.3864 -0.3769 -0.3376 -0.3203 -0.2916 -0.2730 -0.2640 -0.2494 -0.2146 -0.1342 -0.1338 -0.1249 -0.1029 -0.0932 -0.0930 -0.0443 -0.0338 -0.0144

-2.5518 -1.2921 2.0524 7.7718 10.6357 14.7046 15.7352 21.7482 24.4136 26.0932 29.0931 31.5329 43.4787 46.0122 50.1979 59.2422 63.2310 66.5500 69.9443 73.6966 77.3100 85.1497 91.4133 96.3590

Distribucion Normal

17, Determine, con un nivel de confianza de 90%, qué tipo de distribución siguen los datos.

Emplee la prueba Chi-Cuadrada y compruebe con Stat;Fit

18.089 13.025 16.93 18.917 17.552 14.954 17.15 16.648 17.803 12.777 11.144 11.779 12.082 13.163 13.435 13.536 14.257 14.257 14.504 14.517 14.658 14.772 15.188 15.21 15.235 15.281 15.663 15.845 15.881 15.959 15.967 16.082 16.162 16.651 16.733 16.751 16.766 16.805 17.02 17.175 17.206

14.601 18.482 18.475 18.737 18.398 17.131 17.12 19.48 14.342 15.501

12.091 19.439 18.064 13.028 10.877 11.747 13.871 16.416 18.055 17.047

1 2 3 4 5 6 7 8 9 10

17.516 15.032 16.39 13.534 13.538 16.26 15.645 18.18 14.458 11.436 i 10.-11 11.-12 12.-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20

12.258 10.816 15.989 14.233 13.217 17.652 17.293 19.408 15.287 16.925 Oi 0 2 1 3 6 9 7 14 7 1

Ei 5 5 5 5 5 5 5 5 5 5

((Ei-Oi)^2)/Ei 5 1.8 3.2 0.8 0.2 3.2 0.8 16.2 0.8 3.2

17.211 17.223 17.239 17.264 17.264 17.497 17.51 17.52 17.551 17.579 17.77 18.129 18.145 18.168 18.345 18.476 18.58 18.93 19.787

La distribucion que siguen estos datos es lognormal

18. Utilice la prueba de Kolmogorov-Smirnov para determinar, con u n nivel de confianza de 90%,

qué tipo de distribución siguen los datos. Compruebe con Stat::Fit.

2.865 2.336 3.42 1.242 3.117 1.904 1.304 5.632 2.285 2.819

4.419 2.201 1.123 3.725 1.283 3.144 2.151 2.941 4.579 3.47

3.681 1.186 3.264 4.317 3.821 3.541 2.953 2.274 3.631 3.158

6.502 3.61 2.219 1.694 0.943 1.494 1.06 1.841 6.574 2.194

1.141 0.753 1.962 3.286 1.713 5.983 7.8 1.651 1.941 1.524

2.773 2.653 2.915 3.698 4.715 1.649 7.621 4.009 3.255 2.105

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

Ri 1.123 1.186 1.242 1.283 1.304 1.904 2.151 2.201 2.274 2.285 2.336 2.819 2.865 2.941 2.953 3.117 3.144 3.158 3.264 3.42 3.47 3.541 3.631 3.681 3.725 3.821

i/n 0.0333 0.0667 0.1000 0.1333 0.1667 0.2000 0.2333 0.2667 0.3000 0.3333 0.3667 0.4000 0.4333 0.4667 0.5000 0.5333 0.5667 0.6000 0.6333 0.6667 0.7000 0.7333 0.7667 0.8000 0.8333 0.8667

i-1/n 0.0000 0.0333 0.0667 0.1000 0.1333 0.1667 0.2000 0.2333 0.2667 0.3000 0.3333 0.3667 0.4000 0.4333 0.4667 0.5000 0.5333 0.5667 0.6000 0.6333 0.6667 0.7000 0.7333 0.7667 0.8000 0.8333

(i/n)-ri -1.0897 -1.1193 -1.1420 -1.1497 -1.1373 -1.7040 -1.9177 -1.9343 -1.9740 -1.9517 -1.9693 -2.4190 -2.4317 -2.4743 -2.4530 -2.5837 -2.5773 -2.5580 -2.6307 -2.7533 -2.7700 -2.8077 -2.8643 -2.8810 -2.8917 -2.9543

ri-(i-1/n) 1.1230 1.1527 1.1753 1.1830 1.1707 1.7373 1.9510 1.9677 2.0073 1.9850 2.0027 2.4523 2.4650 2.5077 2.4863 2.6170 2.6107 2.5913 2.6640 2.7867 2.8033 2.8410 2.8977 2.9143 2.9250 2.9877

i

2.299 3.574 4.282 3.208 1.74 4.02 2.872 2.54 1.372 2.806

D+

-1.0897

4.589 3.588 4.835 1.628 2.769 1.475 1.474 2.669 2.284 4.819

D-

27 28 29 30

4.317 4.419 4.579 5.632

0.9000 0.9333 0.9667 1.0000

0.8667 0.9000 0.9333 0.9667

-3.4170 -3.4857 -3.6123 -4.6320

3.4503 3.5190 3.6457 4.6653

4.6653


Los datos siguen una distribucion binormal

7.142 3.128 3.057 3.704 2.877 1.802 2.18 1.539 4.499 1.946

D

1.783 3.1 1 1.02 3.956 1.569 2.395 1.917 4.037 3.197

4.6653

los numeros

19, Determine, con un nivel de confianza de 90%, qué tipo de distribución siguen los da-tos usando

la pruebo do Kolmogorov-Smirnov. Compruebe con Stat::Fit.

174.847 119.609 244.874 40.973 205.085 82.842 44.148 647.174 114.911 169.609

i 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

402.174 107.279 35.337 288.761 43.048 208.481 102.905 183.747 431.138 251.844

282.143 38.269 223.936 384.365 303.22 261.858 185.161 113.87 274.864 210.369

859.252 271.768 108.878 67.65 27.863 54.809 32.573 78.092 877.946 106.671

36.146 21.4 87.316 226.819 68.959 989.3 1231.86 64.731 85.668 56.651

164.428 151.421 180.701 284.664 456.507 64.625 1176.46 332.889 222.815 98.984

Ri 35.337 38.269 40.973 43.048 44.148 82.842 102.905 107.279 113.87 114.911 119.609 169.609 174.847 183.747 185.161 205.085 208.481 210.369 223.936 244.874 251.844 261.858 274.864 282.143 288.761 303.22

i/n 0.0333 0.0667 0.1000 0.1333 0.1667 0.2000 0.2333 0.2667 0.3000 0.3333 0.3667 0.4000 0.4333 0.4667 0.5000 0.5333 0.5667 0.6000 0.6333 0.6667 0.7000 0.7333 0.7667 0.8000 0.8333 0.8667

i-1/n 0.0000 0.0333 0.0667 0.1000 0.1333 0.1667 0.2000 0.2333 0.2667 0.3000 0.3333 0.3667 0.4000 0.4333 0.4667 0.5000 0.5333 0.5667 0.6000 0.6333 0.6667 0.7000 0.7333 0.7667 0.8000 0.8333

(i/n)-ri -35.3037 -38.2023 -40.8730 -42.9147 -43.9813 -82.6420 -102.6717 -107.0123 -113.5700 -114.5777 -119.2423 -169.2090 -174.4137 -183.2803 -184.6610 -204.5517 -207.9143 -209.7690 -223.3027 -244.2073 -251.1440 -261.1247 -274.0973 -281.3430 -287.9277 -302.3533

ri-(i-1/n) 35.3370 38.2357 40.9063 42.9480 44.0147 82.6753 102.7050 107.0457 113.6033 114.6110 119.2757 169.2423 174.4470 183.3137 184.6943 204.5850 207.9477 209.8023 223.3360 244.2407 251.1773 261.1580 274.1307 281.3763 287.9610 302.3867

116.195 266.496 378.203 216.767 70.826 334.56 175.667 139.595 47.822 168.127

432.915 268.621 479.587 63.229 164.015 53.719 53.632 153.12 114.754 476.397

D+

D-

-35.3037

27 28 29 30

384.365 402.174 431.138 647.174

0.9000 0.9333 0.9667 1.0000

0.8667 0.9000 0.9333 0.9667

-383.4650 -401.2407 -430.1713 -646.1740

383.4983 401.2740 430.2047 646.2073

646.2073


1034.5 206.518 197.647 285.525 176.297 75.188 105.45 57.566 416.533 86.082

D

73.83 203.016 30.094 30.911 324.298 59.444 125.164 83.781 337.344 215.32

646.2073

an los numeros

Los fatos siguen una distribucion lognormal y exponencial.

20. A partir de la prueba de Kolmogorov-Smirnov, determine con un nivel de confianza de

90% qué tipo de distribución siguen los datos. Compruebe con Stat::Fit. 0.488 0.995 0.088 0.149 0.731 0.591 0.745 0.307 0.084 0.967

0.116 0.908 0.382 0.427 0.313 0.781 0.005 0.692 0.08 0.28

0.731 0.183 0.707 0.743 0.908 0.85 0.256 0.905 0.16 0.333

0.094 0.146 0.413 0.434 0.845 0.048 0.845 0.046 0.028 0.531

0.684 0.633 0.581 0.26 0.937 0.58 0.445 0.128 0.714 0.285

0.093 0.567 0.254 0.738 0.607 0.346 0.777 0.766 0.454 0.504

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

Ri 0.005 0.08 0.084 0.088 0.116 0.149 0.16 0.183 0.256 0.28 0.307 0.313 0.333 0.382 0.427 0.488 0.591 0.692 0.707 0.731 0.731 0.743 0.745 0.781 0.85 0.905 0.908 0.908 0.967

i/n 0.0333 0.0667 0.1000 0.1333 0.1667 0.2000 0.2333 0.2667 0.3000 0.3333 0.3667 0.4000 0.4333 0.4667 0.5000 0.5333 0.5667 0.6000 0.6333 0.6667 0.7000 0.7333 0.7667 0.8000 0.8333 0.8667 0.9000 0.9333 0.9667

i-1/n 0.0000 0.0333 0.0667 0.1000 0.1333 0.1667 0.2000 0.2333 0.2667 0.3000 0.3333 0.3667 0.4000 0.4333 0.4667 0.5000 0.5333 0.5667 0.6000 0.6333 0.6667 0.7000 0.7333 0.7667 0.8000 0.8333 0.8667 0.9000 0.9333

(i/n)-ri 0.0283 -0.0133 0.0160 0.0453 0.0507 0.0510 0.0733 0.0837 0.0440 0.0533 0.0597 0.0870 0.1003 0.0847 0.0730 0.0453 -0.0243 -0.0920 -0.0737 -0.0643 -0.0310 -0.0097 0.0217 0.0190 -0.0167 -0.0383 -0.0080 0.0253 -0.0003

ri-(i-1/n) 0.0050 0.0467 0.0173 -0.0120 -0.0173 -0.0177 -0.0400 -0.0503 -0.0107 -0.0200 -0.0263 -0.0537 -0.0670 -0.0513 -0.0397 -0.0120 0.0577 0.1253 0.1070 0.0977 0.0643 0.0430 0.0117 0.0143 0.0500 0.0717 0.0413 0.0080 0.0337

i

0.368 0.058 0.44 0.3 0.025 0.723 0.896 0.366 0.913 0.837

D+

0.09 0.507 0.447 0.302 0.302 0.787 0.245 0.513 0.666 0.681

D-

0.1003

0.1253

30

0.995

1.0000

0.9667

0.0050

0.0283

En tablas 0.220 Como 0.22<0.1253 se rechaza los numeros

Los datos siguen una distribucion uniforme y lognormal

0.761 0.78 0.251 0.314 0.608 0.535 0.335 0.302 0.213 0.209

D

0.1253

0.42 0.139 0.87 0.423 0.078 0.61 0.194 0.833 0.373 0.626

los numeros

2 1. Determine, con un nivel de confianza de 90%, si la variable aleatoria representada por la

siguiente tabla de frecuencia sigue una distribución exponencial con media 1.

35

Intervalo 0--1 1--2 2--3 3--4 4--5 5--6 6--7 7--8 8--9 9--10 10--?

Frecuencia 29 18 18 12 8 3 2 5 3 0 2

30 25 20 15 10 5 0 0--1

1--2

2--3

3--4

4--5

H0: Exponencial H1: Otra Distribucion

Intervalo 0--1 1--2 2--3 3--4 4--5 5--6 6--7 7--8 8--9 9--10 10--?

Oi 29 18 18 12 8 3 2 5 3 0 2

Poi 0.29 0.18 0.18 0.12 0.08 0.03 0.02 0.05 0.03 0 0.02

Total

100

1

El valor estadistico es C=0.3947 D0.1,100 = 0.1220

POAi 0.29 0.47 0.65 0.77 0.85 0.88 0.9 0.95 0.98 0.98 1

PEAi 0.6321 0.8647 0.9502 0.9817 0.9933 0.9975 0.9991 0.9997 0.9999 1 1

[POAi - PEAi] 0.3421 0.3947 0.3002 0.2117 0.1433 0.1175 0.0991 0.0497 0.0199 0.02 0

C

0.3947

5--6

6--7

7--8

Se rechaza la hipotesis de que los numeros siguen una distribucion Exponencial.

Series1

7--8

8--9 9--10 10--?


datos; emplee la prueba de Anderson-Darling y compruebe con Stat::Fit.

Intervalo ?-12 12.0-12.5 12.5-13.0 13.0-13.5 13.5-14.0 14.0-14.5 14.5-15.0 15.0-15.5 15.5-16.0 16.0-16.5 16.5-17.0 17.0-?

Frecuencia 3 4 3 6 8 15 12 13 7 16 7 6

18 16 14 12 10 8 6 4 2 0

Series1

23. Determine, con un nivel de confianza de 95%, qué tipo de distribución

siguen los datos. Utilice la prueba Chi-Cuadrada,

Intervalo ?--150 150--151 151--152 152--153 153--154 154--155 155--156 156--157 157--158 158--159 159--160 160--?

Frecuencia 0 13 8 11 15 7 8 9 11 10 8 0

1 2 3 4 5 6 7 8 9 10 11 12

i ?--150 150--151 151--152 152--153 153--154 154--155 155--156 156--157 157--158 158--159 159--160 160--?

Total

Oi 0 13 8 11 15 7 8 9 11 10 8 0

Ei 8.33 8.33 8.33 8.33 8.33 8.33 8.33 8.33 8.33 8.33 8.33 8.33

((Ei-Oi)^2)/Ei 8.330 2.618 0.013 0.856 5.341 0.212 0.013 0.054 0.856 0.335 0.013 8.330

100

99.96

26.971

En tablas 4.575 con grados de libertad de 11 y con un 95% de confiabilidad. Por lo tanto como 4.575 <26.971 no se aceptan los numeros como numeros aleatorios.

24. Determine con un nivel de confianza de 90%r qué tipo de distribución

siguen los datos; emplee la prueba Chi-Cuadrada.

Intervalo 0--2 2--4 4--6 6--8 8--10 10--12 12--14 14--16 16--18 18--20 20--22

Frecuencia 39 57 47 23 18 9 2 3 1 1 0 200

1 2 3 4 5 6 7 8 9 10 11 Total

i 0--2 2--4 4--6 6--8 8--10 10--12 12--14 14--16 16--18 18--20 20--22

Oi 39 57 47 23 18 9 2 3 1 1 0

Ei 18.18 8.33 8.33 8.33 8.33 8.33 8.33 8.33 8.33 8.33 8.33

((Ei-Oi)^2)/Ei 23.843 284.366 179.516 25.835 11.226 0.054 4.810 3.410 6.450 6.450 8.330

200

101.48

554.291

Los datos siguen una distribucion lognormal.

25. Utilice la prueba de Kolmogorov-Smirnov para determinar con un nivel de confianza de 95% qué tipo de distribució

4 4 4 3 2 7 5 6 3 1

5 6 4 4 5 2 5 4 3 2

3 4 3 5 3 4 5 6 2 5

5 3 3 2 4 4 2 6 5 2

5 5 3 3 4 2 4 2 3 3

4 2 2 4 1 4 4 4 5 1

3 2 2 3 4 1 5 4 1 5

2 3 3 3 5 5 4 2 3 3

4 3 2 5 4 4 4 2 2 2

3 4 3 3 5 4 1 2 4 5 100

No:

Intervalos 0 2 4 6

-

1 3 5

α

Oi

Poi POAi

6 43 46 5 100

0.06 0.43 0.46 0.05 1.00

Tomando como base: α: 1.38 ß: 5.19

0.06 0.49 0.95 1.00

PEAi

POAi - PEAi

0.09792 0.37459 0.61319 1.00000 c=

-0.0379 0.1154 0.3368 0.0000 0.4143

0.136

MEDIA MUESTRAL VARIANZA

confianza de 95% qué tipo de distribución siguen los datos.

3.49 1.7676

50

45 40

35 30 25

20 15

10 5

0 α

1

3

5

-

-

-

-

0

2

4

6

26. Determine, con un nivel de confianza de 90%, qué tipo de distribución siguen los da-tos usando la prueba de Kolm

1 0 0 1 1 0 1 1 1 0

0 0 0 0 0 1 2 0 0 0 H0 H1

0 0 1 1 1 1 0 1 0 0

1 1 0 2 2 0 1 2 0 1

0 0 0 1 0 0 1 0 0 0

0 0 0 1 0 1 1 0 0 1

1 0 0 1 1 1 0 1 0 2

0 0 0 0 1 2 1 2 0 1

0 0 1 0 0 1 0 1 1 0

0 0 1 0 1 0 1 0 0 0

Intervalo 0 1 2

Oi 56 37 7

POi 0.56 0.37 0.07

POAi 0.56 0.93 1

Es una distribución Poisson Es otra distribución 60

media= varianza= n= m= α=

0.5100 0.39384 100 3 5 %

50 40 30 20

c

D 0.05,100 0.0405 < 0.1360

No podemos rechazar la hipotesis

10 0 0

1

PEAi 0.6005 0.9067 0.9848 c

os usando la prueba de Kolmogorov-Smirnov

|POAi - PEAi| 0.0405 0.0233 0.0152 0.0405

2

0.4119 0.3210 0.3063

27. Determine, con un nivel de confianza de 90%, qué tipo de distribución siguen los da-tos; use la prueba de Kolmogorov-Smirnov y co

5 3 11 4 5 1 7 4 4 5

3 2 5 7 4 4 6 5 5 7

2 4 9 7 5 5 4 5 4 3

4 6 3 3 3 4 6 2 6 7

6 2 7 3 6 6 4 4 2 0

4 8 4 4 4 2 5 2 5 4

3 6 7 8 4 5 4 3 7 5

2 3 2 4 3 5 2 6 5 7

2 0 3 3 7 3 2 7 1 3 4 8 2 5 3 5 4 6 5 11 No: 100

MEDIA MUESTRAL VARIANZA

45 40 35 30 25 20 15

Intervalos

Oi

Poi POAi

0 2 4 6 8 10 12

4 29 40 21 4 2 0 100

0.04 0.29 0.40 0.21 0.04 0.02 0.00 1.00

PEAi

POAi - PEAi

0.09792 0.37459 0.61319 0.77934 0.88206 0.94037 1.00000 c=

-0.0579 -0.0446 0.1168 0.1607 0.0979 0.0596 0.0000 0.3325

10 5

-

1 3 5 7 9 11

α

Tomando como base: α: 1.38 ß: 5.19

0.04 0.33 0.73 0.94 0.98 1.00 1.00

0.1

0

os da-tos; use la prueba de Kolmogorov-Smirnov y compruebe con Stat::Fit

4.46 4.2913

0-1

2-3 4-5 6-7 8-9 10 - 11 12 - α

STAT::FIT

28. Determine, con un nivel de confianza de 90%, qué tipo de distribución siguen los da tos. Use la prueba de Kolmogorov-Smirn

10 14 8 9 4 12 9 11 9 7

9 15 7 12 12 11 14 8 9 9

H0 H1

8 10 9 8 13 10 16 11 6 12 10 5 10 9 8 9 10 8 10 5 3 15 7 5 9 14 12 11 13 7 7 7 18 5 9 14 9 13 14 10 10 10 11 5 11 2 10 15 4 5 9 11 11 7 10 13 8 4 9 8 13 12 15 13 10 11 6 9 10 15

13 12 13 10 10 15 15 5 15 7

Intervalo 1 - 2 3 - 4 5 - 6 7 - 8 9 - 10 11 - 12 13 - 14 15 - 16 17 - 18

Oi 1 4 9 16 31 16 13 9 1

POi 0.01 0.04 0.09 0.16 0.31 0.16 0.13 0.09 0.01

POAi 0.01 0.05 0.14 0.3 0.61 0.77 0.9 0.99 1

PEAi 0.0030 0.0312 0.1366 0.3442 0.5955 0.8009 0.9216 0.9750 0.9935 c

Es una distribución Poisson Es otra distribución 35

= = n= m= α=

9.9000 10.45455 100 9 5 %

30 25 20 15

c

D 0.05,100 0.0442 < 0.1360


10 5 0 2

4

6

8

10

12

14

prueba de Kolmogorov-Smirnov y compruebe con la herramienta Stat::Fit.

STAT::FIT |POAi - PEAi| 0.0070 0.0188 0.0034 0.0442 0.0145 0.0309 0.0216 0.0150 0.0065 0.0442

16

18

29. A partir de la prueba Chi-Cuadrada, determine con un nivel de confianza de 90% qué tipo de distribución siguen los datos

2 1 1 2 1 2 1 1 0 1

H0 H1

1 2 1 0 1 0 2 1 1 2

2 2 0 0 1 3 3 1 0 0

0 1 2 1 1 2 0 0 1 0

1 0 2 2 2 0 0 2 0 1

1 0 0 1 1 0 0 0 1 1

Es una distribución Poisson Es otra distribución

media= varianza= n= intervalos= nivel confianza α=

0.9600 0.74586 100 4 10 %

2 0 0 0 1 1 0 0 1 0

1 0 2 0 1 2 1 0 2 0

0 1 1 2 2 1 1 3 3 2

1 1 0 2 0 1 0 1 2 0

Intervalos Oi 0 1 2 3

35 0.3829 38 0.3676 23 0.1764 4 0.0565 100 0.983367

40 35 30 25 20 15 10 5

c 2.4305

X² 0.1,3 6.2514

< No podemos rechazar la hipotesis

P(x)

0 0

tribución siguen los datos

Ei(x) 38.2893 36.7577 17.6437 5.6460 C=

1

(Ei-Oi)²/Ei 0.2826 0.0420 1.6261 0.4799 2.4305

2

3

30. Determine, con un nivel de confianza de 90% qué tipo de distribución siguen los datos; emplee la prueba Chi-Cuadrada.

0 0 0 0 1 0 0 0 1 0

0 0 1 0 0 0 1 0 1 1

0 1 1 0 0 0 1 0 0 0

0 0 0 0 1 0 1 0 0 0

0 1 0 0 0 0 0 0 0 0

0 0 1 0 0 1 0 0 1 0

0 1 1 0 0 0 1 1 0 0

1 0 1 0 1 0 0 0 0

1

0 1 0 0 1 1 0 0 0 0

0 0 1 0 0 1 0 0 0 0

Intervalo 0 1

80 70

Oi 72 28

P(x) 0.7000 0.3000 1.0000

Ei 70.0000 30.0000 C=

72

60 50

H0 H1

Es una distribución Binomial Es otra distribución

40 28

30 20

n= 100 m= 2 α= 10 %

c

X² 0.1,1 0.1905 < 2.7055


10 0 1

prueba Chi-Cuadrada.

(Ei-Oi)²/Ei 0.0571 0.1333 0.1905

31. Determine, con un niveI de confianza de 95%, qué tipo de distribución siguen los datos; emplee la prueba Chi-cuadrada

8 8 6 7 6 4 6 5 5 4

H0 H1

8 8 8 5 8 5 5 7 6 4

6 5 6 8 8 6 7 6 6 4

6 4 8 7 5 5 4 6 5 4

4 6 7 6 6 8 7 5 8 7

7 5 5 8 7 4 8 5 4 7


5 4 4 5 4 5 8 6 8 8

4 4 6 5 4 8 4 5 5 8

6 6 5 4 7 4 5 5 6 5

6 4 6 7 6 8 4 5 7 7

Intervalos Oi 4 5 6 7 8

P(x)

21 0.1401 24 0.1642 22 0.1604 14 0.1342 19 0.0983 100 0.697210

30 25


5.8600 1.98020 100 5 5 %

20 15 10 5

c 17.7777

X² 0.05,4 9.4877 > Se rechaza la hipotesis

0 4

5

la prueba Chi-cuadrada

Ei(x) 14.0092 16.4188 16.0357 13.4242 9.8332 C=

5

(Ei-Oi)²/Ei 3.4885 3.5005 2.2184 0.0247 8.5456 17.7777

6

7

8

32. Utilce la prueba Chi-cuadrada para determinar, con un nivel de confianza de 95%, qué tipo de distribución siguen Ios datos. C

1 2 1 0 0 0 0 0 0 1

2 1 1 1 1 0 0 2 2 1

0 1 2 0 1 2 0 2 2 0

1 1 1 0 1 0 1 1 0 1

2 1 1 1 0 0 1 0 1 0

1 2 0 0 0 0 0 1 3 0

0 0 0 2 0 2 0 2 1 1

0 2 0 0 0 0 1 1 2 1

1 2 1 1 1 1 0 2 0 2

2 1 1 2 0 2 2 1 1 2

Intervalo 0 1 2 3

Oi 38 38 23 1 100

P(x) 0.4190 0.3645 0.1586 0.0460 0.9880

Ei (Ei-Oi)²/Ei 41.8952 0.3621 36.4488 0.0660 15.8552 3.2196 4.5980 2.8155 C= 6.4633

40

H0 H1

Es una distribución Poisson Es otra distribución = = n= m= α=

0.8700 0.63949 100 4 5 %

35 30 25 20 15 10 5 0 0

c

X² 0.05,3 6.4633 < 7.8147


1

2

3

e distribución siguen Ios datos. Compruebe con Stat:fit

3

STAT::FIT

33. Determine, con un nivel de confianza de 90%, qué tipo de distribución siguen los datos. Utilice la prueba de Kolmogorov-Smirn

4 5 3 3 5 4 5 3 3 5

5 5 3 5 5 4 5 4 4 5

4 4 4 5 4 5 5 4 3 3

4 4 5 5 5 3 3 5 4 4

4 3 3 5 4 3 5 3 3 5

4 5 5 3 5 3 3 3 5 4

5 5 4 5 5 5 5 4 3 5

4 4 4 5 4 4 4 2 5 5

5 4 4 3 4 5 4 5 5 5

3 5 5 3 4 4 4 5 3 4

Intervalos Oi 2 3 4 5

P(x)

1 0.1343 23 0.1867 34 0.1947 42 0.1624 100 0.678140

45

H0 H1


40 35 30


4.1700 0.66778 100 4 10 %

25 20 15 10 5 0 2

c 64.2393


3

la prueba de Kolmogorov-Smirnov y compruebe con Stat::Fit

Ei(x) 13.4349 18.6745 19.4682 16.2364 C=

4

(Ei-Oi)²/Ei 11.5093 1.0019 10.8472 40.8809 64.2393

5

STAT::FIT

34. Determine, con un nivel de confianza de 95%, qué tipo de distribución siguen los datos; emplee la prueba Chi-cuadrada y com

H0 H1

Es una distribución Poisson Es otra distribución = = n= m= α=

c

1.9900 100 6 5 %

X² 0.05,5 3.7647 < 11.0705

Suma 0 29 62 42 36 30 199

Intervalo 0 1 2 3 4 5

Oi 11 29 31 14 9 6

P(x) 0.1367 0.272 0.2707 0.1795 0.0893 0.0355 0.9838

0

1

2

Ei 13.66954 27.20239 27.06638 17.95403 8.93213 3.554988

(Ei-Oi)²/Ei 0.521338 0.118791 0.571683 0.870799 0.000516 1.681605 3.764732

35 30


25 20 15 10 5 0 3

4

5

prueba Chi-cuadrada y compruebe con Stat: :Fit

5

STAT::FIT

35. Determine, con un nivel de confianza de 90%, qué tipo de distribución siguen los datos; use la prueba Chi-cuadrada. Comprue

0 6 1 2 0 4 1 0 7 0

H0 H1

1 0 2 2 1 2 1 5 0 0

0 0 1 2 0 0 0 0 0 5

2 3 1 1 2 8 2 1 0 1

1 1 4 0 1 0 0 1 2 2

0 4 0 0 0 2 0 1 0 4

2 0 0 0 0 0 0 0 2 0

5 0 0 4 9 6 3 1 0 0

0 2 1 3 3 1 1 0 2 0

Intervalos Oi 0 1 2 3 4 5 6 7 8 9

1.4900 4.17162 100 10 10 %


P(x)

44 0.2254 20 0.3358 17 0.2502 5 0.1243 5 0.0463 3 0.0138 2 0.0034 1 0.0007 1 0.0001 2 0.0000 100 0.999996



c 1901.6251

2 0 0 0 0 1 3 0 2 9

50 45 40 35 30 25 20 15 10 5 0 0

1

2

3

4

5

prueba Chi-cuadrada. Compruebe con Stat::Fit

Ei(x)

(Ei-Oi)²/Ei

22.5373 20.4394 33.5805 5.4922 25.0175 2.5694 12.4254 4.4374 4.6284 0.0298 1.3793 1.9044 0.3425 8.0207 0.0729 11.7888 0.0136 71.6562 0.0022 1775.2867 C= 1901.6251

5

6

7

8

9

STAT::FIT

36. Emplee la prueba Ch i cuadrada para determinar, con un nivel de confianza de 90%, qué tipo de distribución siguen los datos.

25 20 15 10 5 0 0

H0 H1

1

2

Es una distribución Geometrica Es otra distribución = = p= n= α=

3.7700 0.5 100 5 %

c X² 0.05,99 12841.1769 > 123.2252 Se rechaza la hipotesis

H0 H1

Es una distribución Geometrica Es otra distribución

media= varianza= p= n= α=

1.3200 0.5 100 5 %

c X² 0.05,99 82.7000 < 123.2252 No podemos rechazar la hipotesis

3

4

5

6

7

8

9

10 11 12 13 14

Intervalo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Oi 21 17 14 9 8 6 6 1 4 4 1 0 1 2 6

P(x) 0.5000 0.2500 0.1250 0.0625 0.0313 0.0156 0.0078 0.0039 0.0020 0.0010 0.0005 0.0002 0.0001 0.0001 0.0000 1.0000

Ei 50.0000 25.0000 12.5000 6.2500 3.1250 1.5625 0.7813 0.3906 0.1953 0.0977 0.0488 0.0244 0.0122 0.0061 0.0031

Intervalo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Oi 21 17 14 9 8 6 6 1 4 4 1 0 1 2 6

P(x) 0.0666667 0.0666667 0.0666667 0.0666667 0.0666667 0.0666667 0.0666667 0.0666667 0.0666667 0.0666667 0.0666667 0.0666667 0.0666667 0.0666667 0.0666667 1.0000

Ei 6.6667 6.6667 6.6667 6.6667 6.6667 6.6667 6.6667 6.6667 6.6667 6.6667 6.6667 6.6667 6.6667 6.6667 6.6667

0%, qué tipo de distribución siguen los datos.

(Ei-Oi)²/Ei 16.82 2.56 0.18 1.21 7.605 12.6025 34.86125 0.950625 74.1153125 155.9376563 18.52882813 0.024414063 79.93220703 651.3661035 11784.48305 12841.17695

(Ei-Oi)²/Ei 30.81666667 16.01666667 8.066666667 0.816666667 0.266666667 0.066666667 0.066666667 4.816666667 1.066666667 1.066666667 4.816666667 6.666666667 4.816666667 3.266666667 0.066666667 82.7

38. Determine, con un nivel de confianza de 90%, si los datos se distribuyen de acuerdo con una distribución uniforme discreta (1

H0 H1


media= varianza= i= j= n= m= α=

3.7600 1 6 100 6 5 %

Suma 13 28 54 56 105 120 376

Intervalo 1 2 3 4 5 6

Oi 13 14 18 14 21 20

P(x) 0.16667 0.16667 0.16667 0.16667 0.16667 0.16667 1

25

c

X² 0.05,5 3.5600 < 11.0705


20

15

10

5

0 1

2

3

4

distribución uniforme discreta (1-6)

Ei 16.6667 16.6667 16.6667 16.6667 16.6667 16.6667

5

(Ei-Oi)²/Ei 0.806666667 0.426666667 0.106666667 0.426666667 1.126666667 0.666666667 3.56

6

47. Utilizando cualquier hoja de cálculo,genere 100 variables aleatorias a) exponencialmente distribuidas con λ = 3. b) normalmente distribuidas con media 10 y varianza 4. c) uniformemente distribuidas con límite inferior igual a 10 y limite superior igual a 30. d) trianguIármente distribuidas con límite inferior = 5, valor mas probable = 10 y limite superior = 15. e) con distribución binomial y parámetros N= 5,p = 0.3, q = 0.7 con distribución de Poisson, con A - 3, f) con distribución de Poisson, con λ = 3. Compruebe con Stat: Fit si las variables aleatorias generadas siguen la distribución de probabilidad que se esperaría de ellas.

Numeros Generado 0.0190 0.0248 0.0321 0.0323 0.0469 0.0561 0.0641 0.0783 0.0935 0.1154 0.1162 0.1173 0.1357 0.1498 0.1503 0.1701 0.1965 0.2168 0.2271 0.2281 0.2314 0.2377 0.2430 0.2475 0.2516 0.2649 0.2772 0.2814 0.2816 0.2897 0.2905 0.2907 0.3031 0.3225 0.3315 0.3383 0.3485 0.3669

a 2.83389 2.78517 2.72442 2.72254 2.60651 2.53503 2.47488 2.37226 2.26593 2.12181 2.11732 2.11024 1.99692 1.91425 1.91099 1.80111 1.66392 1.56543 1.51790 1.51325 1.49862 1.47037 1.44718 1.42783 1.41038 1.35512 1.30592 1.28977 1.28900 1.25805 1.25503 1.25425 1.20851 1.14011 1.10979 1.08736 1.05446 0.99799

b 0.05537 0.07161 0.09186 0.09249 0.13116 0.15499 0.17504 0.20925 0.24469 0.29273 0.29423 0.29659 0.33436 0.36192 0.36300 0.39963 0.44536 0.47819 0.49403 0.49558 0.50046 0.50988 0.51761 0.52406 0.52987 0.54829 0.56469 0.57008 0.57033 0.58065 0.58166 0.58192 0.59716 0.61996 0.63007 0.63755 0.64851 0.66734

0.00629 0.00632 0.00635 0.00635 0.00642 0.00646 0.00650 0.00656 0.00663 0.00673 0.00674 0.00674 0.00683 0.00690 0.00690 0.00700 0.00713 0.00723 0.00728 0.00728 0.00730 0.00733 0.00736 0.00738 0.00740 0.00747 0.00754 0.00756 0.00756 0.00760 0.00760 0.00761 0.00767 0.00777 0.00782 0.00786 0.00791 0.00801

f 0.02004 0.01961 0.01907 0.01906 0.01807 0.01748 0.01699 0.01619 0.01538 0.01434 0.01431 0.01426 0.01348 0.01293 0.01291 0.01220 0.01137 0.01080 0.01053 0.01050 0.01042 0.01027 0.01014 0.01004 0.00994 0.00965 0.00940 0.00932 0.00931 0.00916 0.00914 0.00914 0.00891 0.00858 0.00844 0.00833 0.00818 0.00793

0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979

0.22404 0.22404 0.22404 0.22404 0.22404 0.22404 0.22404 0.22404 0.22404 0.22404 0.22404 0.22404 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.14936 0.04979

0.3836 0.3986 0.4038 0.4039 0.4094 0.4109 0.4603 0.4826 0.4938 0.4938 0.4945 0.4973 0.5175 0.5402 0.5511 0.5524 0.5750 0.5780 0.6004 0.6110 0.6163 0.6240 0.6351 0.6576 0.6708 0.6735 0.6789 0.7261 0.7447 0.7514 0.7650 0.7811 0.7935 0.8089 0.8359 0.8363 0.8408 0.8621 0.8744 0.8746 0.8754 0.8846 0.8849 0.8965 0.9009 0.9102 0.9148 0.9311 0.9355 0.9403 0.9508 0.9524

0.94918 0.90750 0.89343 0.89299 0.87849 0.87458 0.75399 0.70518 0.68193 0.68192 0.68053 0.67491 0.63507 0.59339 0.57417 0.57194 0.53459 0.52978 0.49530 0.47981 0.47227 0.46151 0.44636 0.41721 0.40100 0.39783 0.39142 0.33975 0.32124 0.31483 0.30228 0.28805 0.27749 0.26498 0.24435 0.24408 0.24080 0.22587 0.21773 0.21759 0.21709 0.21112 0.21098 0.20374 0.20105 0.19557 0.19283 0.18367 0.18127 0.17868 0.17311 0.17230

0.68361 0.69750 0.70219 0.70234 0.70717 0.70847 0.74867 0.76494 0.77269 0.77269 0.77316 0.77503 0.78831 0.80220 0.80861 0.80935 0.82180 0.82341 0.83490 0.84006 0.84258 0.84616 0.85121 0.86093 0.86633 0.86739 0.86953 0.88675 0.89292 0.89506 0.89924 0.90398 0.90750 0.91167 0.91855 0.91864 0.91973 0.92471 0.92742 0.92747 0.92764 0.92963 0.92967 0.93209 0.93298 0.93481 0.93572 0.93878 0.93958 0.94044 0.94230 0.94257

0.00811 0.00819 0.00822 0.00822 0.00825 0.00826 0.00854 0.00867 0.00874 0.00874 0.00874 0.00876 0.00888 0.00902 0.00908 0.00909 0.00923 0.00925 0.00939 0.00946 0.00949 0.00954 0.00961 0.00976 0.00984 0.00986 0.00990 0.01021 0.01034 0.01039 0.01048 0.01059 0.01068 0.01079 0.01098 0.01098 0.01102 0.01117 0.01126 0.01126 0.01127 0.01134 0.01134 0.01143 0.01146 0.01153 0.01156 0.01169 0.01172 0.01176 0.01184 0.01185

0.00771 0.00753 0.00747 0.00747 0.00741 0.00739 0.00690 0.00670 0.00661 0.00661 0.00661 0.00659 0.00644 0.00628 0.00621 0.00620 0.00607 0.00605 0.00593 0.00587 0.00585 0.00581 0.00576 0.00566 0.00560 0.00559 0.00557 0.00540 0.00534 0.00532 0.00528 0.00523 0.00520 0.00516 0.00510 0.00509 0.00508 0.00504 0.00501 0.00501 0.00501 0.00499 0.00499 0.00497 0.00496 0.00495 0.00494 0.00491 0.00490 0.00489 0.00488 0.00488

0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979

0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979

0.9585 0.9610 0.9629 0.9680 0.9716 0.9724 0.9725 0.9816 0.9907 0.9995

0.16915 0.16789 0.16692 0.16439 0.16264 0.16223 0.16220 0.15785 0.15358 0.14957

0.94362 0.94404 0.94436 0.94520 0.94579 0.94592 0.94593 0.94738 0.94881 0.95014

0.01190 0.01192 0.01193 0.01197 0.01200 0.01201 0.01201 0.01208 0.01215 0.01222

0.00487 0.00486 0.00486 0.00485 0.00485 0.00485 0.00485 0.00483 0.00482 0.00481

0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979

0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979 0.04979

y limite superior = 15. n de Poisson, con A - 3,

e 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807

0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807

0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807 0.16807

F) 0.9629 0.9610 0.9716 0.0641 0.3485 0.1173 0.2907 0.9355 0.2281 0.9816

0.1357 0.7514 0.9725 0.8746 0.9009 0.1154 0.0561 0.5524 0.6789 0.2314

Intervalo 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

-

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.4938 0.8621 0.0323 0.5402 0.4945 0.2897 0.2475 0.0935 0.9907 0.3669

0.0248 0.9524 0.6351 0.5511 0.7650 0.8846 0.2271 0.6004 0.8849 0.1701

0.6163 0.3836 0.1498 0.4826 0.8408 0.8965 0.9680 0.2516 0.3315 0.6240

Oi

P(x)

Ei(x)

9 8 15 8 10 6 9 6 11 18

0.10536 0.11759 0.13124 0.14649 0.1635 0.18248 0.20367 0.22732 0.25372 0.28318

10.5356 11.7590 13.1245 14.6485 16.3496 18.2481 20.3671 22.7322 25.3720 28.3183

0.6110 0.0190 0.4603 0.9995 0.3383 0.2814 0.9585 0.7261 0.6576 0.1503

C 0.0212 0.1022 0.0204 0.2060 0.1508 0.4505 0.3115 0.5418 0.3209 0.1328

100 1.81455 181.455 2.25808

0.1162 0.9403 0.4094 0.9148 0.6735 0.4938 0.4973 0.0321 0.0783 0.6708

0.9311 0.9102 0.0469 0.8363 0.3225 0.7811 0.2430 0.8359 0.5750 0.8754

0.4039 0.9508 0.5780 0.3986 0.2816 0.2649 0.8744 0.7447 0.5175 0.7935

0.3031 0.2168 0.2905 0.9724 0.2772 0.8089 0.1965 0.4109 0.2377 0.4038

Simulacion Promodel Ejercicios Unidad 3

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