estrella simu

Xi RiX0 93 0.3647X1 159 0.6235X2 181 0.7098X3 103 0.4039X4 77 0.3020X5 239 0.9373X6 37 0.1451X7 55 0.2157X8 61 0.2392X9 63 0.2471X10 149 0.5843X11 7 0.0275X12 45 0.1765X13 143 0.5608X14 5 0.0196X15 215 0.8431X16 29 0.1137X17 223 0.8745X18 117 0.4588X19 167 0.6549X20 13 0.0510

Genere nmeros pseudoaleatorios 0-1, X0 = 57; k = 5 y g = 8, hasta encontrar el ciclo de vida.

_(+ )=() )( , , , , ,= ============ ^ = + = + =+ =+=, , , = = = = = = = = = = = _: :

:=/============ ^( )

_=_/( )

ALGORITMO CONGRUENCIAL

MULTIPLICATIVO

X21 47 0.1843X22 229 0.8980X23 119 0.4667X24 253 0.9922X25 127 0.4980X26 85 0.3333X27 71 0.2784X28 237 0.9294X29 207 0.8118X30 197 0.7725X31 23 0.0902X32 221 0.8667X33 31 0.1216X34 53 0.2078X35 231 0.9059X36 205 0.8039X37 111 0.4353X38 165 0.6471X39 183 0.7176X40 189 0.7412X41 191 0.7490X42 21 0.0824X43 135 0.5294X44 173 0.6784X45 15 0.0588X46 133 0.5216X47 87 0.3412X48 157 0.6157X49 95 0.3725X50 245 0.9608X51 39 0.1529X52 141 0.5529X53 175 0.6863X54 101 0.3961X55 247 0.9686X56 125 0.4902X57 255 1.0000X58 213 0.8353X59 199 0.7804X60 109 0.4275X61 79 0.3098X62 69 0.2706X63 151 0.5922X64 93 0.3647X65 159 0.6235

El ciclo de vida es 64.N = 64

DATOSX0 93k 5g 8m 256

a = 3+8k 43N 64

MEDIA 0.5093


_( ++++++++++++ )=() )(=, , , , ,= = = = = = = = = = = ============ ^ = + = + =+ =+=, , , = = = = = = = = = = = _: :

:=/============ ^( )

_=_/( )


_( ++++++++++++ )=() )(=, , , , ,= = = = = = = = = = = ============ ^ = + = + =+ =+=, , , = = = = = = = = = = = _: :

:=/============ ^( )

_=_/( )

Xi Ri NIVEL DE CONFIANZAX1 0.6235 95%X2 0.7098X3 0.4039X4 0.3020 0.05X5 0.9373X6 0.1451 NX7 0.2157 64X8 0.2392X9 0.2471X10 0.5843X11 0.0275X12 0.1765X13 0.5608X14 0.0196X15 0.8431X16 0.1137X17 0.8745X18 0.4588X19 0.6549

X20 0.0510X21 0.1843X22 0.8980X23 0.4667X24 0.9922X25 0.4980X26 0.3333X27 0.2784X28 0.9294X29 0.8118X30 0.7725X31 0.0902X32 0.8667X33 0.1216X34 0.2078X35 0.9059X36 0.8039X37 0.4353X38 0.6471X39 0.7176X40 0.7412X41 0.7490X42 0.0824X43 0.5294X44 0.6784X45 0.0588X46 0.5216X47 0.3412X48 0.6157X49 0.3725X50 0.9608X51 0.1529X52 0.5529X53 0.6863X54 0.3961X55 0.9686X56 0.4902X57 1.0000X58 0.8353X59 0.7804X60 0.4275X61 0.3098X62 0.2706X63 0.5922X64 0.3647

MEDIA TERICA0.50 Hallar el limite superior, central e inferior

Z TEORICO1.96

N64

INTERPRETACION :

_ ============ /+ _(/) (/ )

_ ============ / _(= )^

_ ============ /_(/) (/ )

Hallar el limite superior, central e inferior

0.570725

0.5098

0.429275

_ ============ /+ _(/) (/ )

_ ============ / _( ============ )^

_ ============ /_(/) (/ )

NIVEL DE CONFIANZA MEDIA TERICA95% 0.50

VARIANZA TERICA0.05 0.0833

MEDIA MUESTRAL SEGN TABLA (X^2)0.5098 154.0183

101.6877N64

Xi RiX1 0.6235 0.0129X2 0.7098 0.0400X3 0.4039 0.0112X4 0.3020 0.0432X5 0.9373 0.1827X6 0.1451 0.1330X7 0.2157 0.0865X8 0.2392 0.0732X9 0.2471 0.0690

X10 0.5843 0.0056X11 0.0275 0.2327X12 0.1765 0.1111X13 0.5608 0.0026X14 0.0196 0.2403X15 0.8431 0.1111X16 0.1137 0.1569X17 0.8745 0.1330X18 0.4588 0.0026X19 0.6549 0.0211X20 0.0510 0.2105X21 0.1843 0.1059

Prueba de Varianza

)(_ ^^^^^^^^^^^^ Hallar el limite superior, central e inferior Hallar el limite superior, central e inferior

_( )( )=(_(/, )^)/( )( )

_( )( )=(_( =)^ () ^ )/( )

_( )( )=(_(/ , )^)/( )( )

X22 0.8980 0.1507X23 0.4667 0.0019X24 0.9922 0.2327X25 0.4980 0.0001X26 0.3333 0.0311X27 0.2784 0.0535X28 0.9294 0.1761X29 0.8118 0.0912X30 0.7725 0.0690X31 0.0902 0.1761X32 0.8667 0.1274X33 0.1216 0.1507X34 0.2078 0.0912X35 0.9059 0.1569X36 0.8039 0.0865X37 0.4353 0.0056X38 0.6471 0.0188X39 0.7176 0.0432X40 0.7412 0.0535X41 0.7490 0.0572X42 0.0824 0.1827X43 0.5294 0.0004X44 0.6784 0.0284X45 0.0588 0.2034X46 0.5216 0.0001X47 0.3412 0.0284X48 0.6157 0.0112X49 0.3725 0.0188X50 0.9608 0.2034X51 0.1529 0.1274X52 0.5529 0.0019X53 0.6863 0.0311X54 0.3961 0.0129X55 0.9686 0.2105X56 0.4902 0.0004X57 1.0000 0.2403X58 0.8353 0.1059X59 0.7804 0.0732X60 0.4275 0.0068X61 0.3098 0.0400X62 0.2706 0.0572X63 0.5922 0.0068X64 0.3647 0.0211

INTERPRETACION :0.2037

0.0853

0.1345

Prueba de Varianza

Hallar el limite superior, central e inferior Hallar el limite superior, central e inferior

Debido a que el valor de V(r) se encuentra entre los lmites de aceptacin, decimos que no se puede rechazar que el conjunto Ri tiene una varianza de 1/12, con un nivel de aceptacin de 95%; de lo contrario, se rechazara que el conjunto Ri tiene una varianza de 1/12

_( )( )=(_(/, )^)/( )( )

_( )( )=(_( =)^ () ^ )/( )

_( )( )=(_(/ , )^)/( )( )

INTERPRETACION :

Debido a que el valor de V(r) se encuentra entre los lmites de aceptacin, decimos que no se puede rechazar que el conjunto Ri tiene una varianza de 1/12, con un nivel de aceptacin de 95%; de lo contrario, se rechazara que el conjunto Ri tiene una varianza de 1/12

Max 1.000000 N

Min 0.019608 m

Rango

nivel de confianza

XiRi

X1 0.6235X2 0.7098X3 0.4039X4 0.3020X5 0.9373X6 0.1451X7 0.2157X8 0.2392X9 0.2471

X10 0.5843X11 0.0275X12 0.1765X13 0.5608X14 0.0196X15 0.8431X16 0.1137X17 0.8745X18 0.4588X19 0.6549X20 0.0510X21 0.1843

Amplitud de intervalos

1-

X22 0.8980X23 0.4667X24 0.9922X25 0.4980X26 0.3333X27 0.2784X28 0.9294X29 0.8118X30 0.7725X31 0.0902X32 0.8667X33 0.1216X34 0.2078X35 0.9059X36 0.8039X37 0.4353X38 0.6471X39 0.7176X40 0.7412X41 0.7490X42 0.0824X43 0.5294X44 0.6784X45 0.0588X46 0.5216X47 0.3412X48 0.6157X49 0.3725X50 0.9608X51 0.1529X52 0.5529X53 0.6863X54 0.3961X55 0.9686X56 0.4902X57 1.0000X58 0.8353X59 0.7804X60 0.4275X61 0.3098X62 0.2706X63 0.5922X64 0.3647

64

8.00

0.9804

0.12254902

0.95

0.05

INTERVALOS

LM inf. LM sup.

1 0.019607843 0.1421568632 0.142156863 0.2647058823 0.2647058824 0.3872549024 0.387254902 0.50980392165 0.5098039216 0.63235294126 0.6323529412 0.75490196087 0.7549019608 0.87745098048 0.8774509804 1

Total

Segun TABLA: CHI CUADRADO14.0714.07

= m=

. =/

_0.05,7^2 ^2 0.05,7_

Oi(Frecuencia observada en cada intervalo)

8 8.0008 8.0008 8.0008 8.0008 8.0008 8.0008 8.0008 8.000

64 0.000

E =N/m

=

. =/

Podemos afirmar que los ri obtenidos a partir del algoritmo multiplicativo siguen una distribucin uniforme, ya que se cumple la condicin necesaria de los pseudoaletorios.

Debido a que el valor del estadstico _0^2 es menor al valor de tablas de _( 1, )^2, entonces no se puede rechazar que el conjunto de nmeros Ri sigue una distribucin uniforme.

0.00000.00000.00000.00000.00000.00000.00000.00001.5000

(Ei - Oi)/E

INTERPRETACION

Podemos afirmar que los ri obtenidos a partir del algoritmo multiplicativo siguen una distribucin uniforme, ya que se cumple la condicin necesaria de los pseudoaletorios.

Debido a que el valor del estadstico _0^2 es menor al valor de tablas de _( 1, )^2, entonces no se puede rechazar que el conjunto de nmeros Ri sigue una distribucin uniforme.

Xi Ri PruebaX1 0.6235 1X2 0.7098 1X3 0.4039 0X4 0.3020 0X5 0.9373 1X6 0.1451 0X7 0.2157 0X8 0.2392 0X9 0.2471 0X10 0.5843 1X11 0.0275 0X12 0.1765 0X13 0.5608 1X14 0.0196 0X15 0.8431 1X16 0.1137 0X17 0.8745 1X18 0.4588 0

Prueba Corrida Arriba y Abajo Media

Determine si la secuencia siguiente de 128 nmeros es tal que la hiptesis de independencia pueda ser rechazada donde = 0.05

DONDE:_ ().= (((((((((((_ ().= (((((((((((_ .=

=_+_

X19 0.6549 1X20 0.0510 0X21 0.1843 0X22 0.8980 1X23 0.4667 0X24 0.9922 1X25 0.4980 0X26 0.3333 0X27 0.2784 0X28 0.9294 1X29 0.8118 1X30 0.7725 1X31 0.0902 0X32 0.8667 1X33 0.1216 0X34 0.2078 0X35 0.9059 1X36 0.8039 1X37 0.4353 0X38 0.6471 1X39 0.7176 1X40 0.7412 1X41 0.7490 1X42 0.0824 0X43 0.5294 1X44 0.6784 1X45 0.0588 0X46 0.5216 1X47 0.3412 0X48 0.6157 1X49 0.3725 0X50 0.9608 1X51 0.1529 0X52 0.5529 1X53 0.6863 1X54 0.3961 0X55 0.9686 1X56 0.4902 0X57 1.0000 1X58 0.8353 1X59 0.7804 1X60 0.4275 0X61 0.3098 0X62 0.2706 0X63 0.5922 1

X64 0.3647 0

n 64n0 32n1 32Co 43alfa 0.05

Z 1.96

43.5

15.746032

Prueba Corrida Arriba y Abajo Media

Determine si la secuencia siguiente de 128 nmeros es tal que la hiptesis de independencia pueda ser rechazada donde = 0.05

DONDE:_ ().= (((((((((((_ ().= (((((((((((_ .=

=_+_

-0.126004

A continuacion se presentan las edades de personas jovenes que van de compras al centro comercial Real Plaza Trujillo.

i Xi max 301 26 min 182 253 24 n 644 22 m 85 21 rango 126 19 amplitud 1.57 208 21 1-alfa 0.959 22 alfa 0.0510 2311 2412 25 INTERVALOS13 26 Limite inferior14 27 1 1815 28 2 19.516 18 3 2117 23 4 22.518 25 5 2419 21 6 25.520 24 7 2721 25 8 28.522 2023 2424 2525 3026 2127 2428 2829 3030 2631 2732 2933 2834 2135 2536 2637 2338 1839 2640 22

1 2 3 4 5 6 7 80

2

4

6

8

10

12

41 2142 2643 2044 2645 1846 2647 2048 2149 2250 2351 2452 2553 2654 2155 2756 2857 2958 1859 2660 2261 2762 2663 2064 25

1 2 3 4 5 6 7 80

2

4

6

8

10

12

A continuacion se presentan las edades de personas jovenes que van de compras al centro comercial Real Plaza Trujillo.

INTERVALOSlimite superior Oi Probabilidad

19.5 4 0.070175438621 6 0.1052631579

22.5 8 0.140350877224 9 0.1578947368

25.5 11 0.192982456127 9 0.1578947368

28.5 7 0.122807017530 3 0.0526315789

57

HISTOGRAMA

1 2 3 4 5 6 7 80

2

4

6

8

10

12

1 2 3 4 5 6 7 80

2

4

6

8

10

12

DISTRIBUCION CHI CUADRADO

Xi Media (X-Xi)^2 Varianza1 26 23.890625 4.44946289 9.813244052 25 23.890625 1.23071289 9.813244053 24 23.890625 0.01196289 9.813244054 22 23.890625 3.57446289 9.813244055 21 23.890625 8.35571289 9.813244056 19 23.890625 23.9182129 9.813244057 20 23.890625 15.1369629 9.813244058 21 23.890625 8.35571289 9.813244059 22 23.890625 3.57446289 9.81324405

10 23 23.890625 0.79321289 9.8132440511 24 23.890625 0.01196289 9.8132440512 25 23.890625 1.23071289 9.8132440513 26 23.890625 4.44946289 9.8132440514 27 23.890625 9.66821289 9.8132440515 28 23.890625 16.8869629 9.8132440516 18 23.890625 34.6994629 9.8132440517 23 23.890625 0.79321289 9.8132440518 25 23.890625 1.23071289 9.8132440519 21 23.890625 8.35571289 9.8132440520 24 23.890625 0.01196289 9.81324405

21 25 23.890625 1.23071289 9.8132440522 20 23.890625 15.1369629 9.8132440523 24 23.890625 0.01196289 9.8132440524 25 23.890625 1.23071289 9.8132440525 30 23.890625 37.3244629 9.8132440526 21 23.890625 8.35571289 9.8132440527 24 23.890625 0.01196289 9.8132440528 28 23.890625 16.8869629 9.8132440529 30 23.890625 37.3244629 9.8132440530 26 23.890625 4.44946289 9.8132440531 27 23.890625 9.66821289 9.8132440532 29 23.890625 26.1057129 9.8132440533 28 23.890625 16.8869629 9.8132440534 21 23.890625 8.35571289 9.8132440535 25 23.890625 1.23071289 9.8132440536 26 23.890625 4.44946289 9.8132440537 23 23.890625 0.79321289 9.81324405

38 18 23.890625 34.6994629 9.8132440539 26 23.890625 4.44946289 9.8132440540 22 23.890625 3.57446289 9.8132440541 21 23.890625 8.35571289 9.8132440542 26 23.890625 4.44946289 9.8132440543 20 23.890625 15.1369629 9.8132440544 26 23.890625 4.44946289 9.8132440545 18 23.890625 34.6994629 9.8132440546 26 23.890625 4.44946289 9.8132440547 20 23.890625 15.1369629 9.8132440548 21 23.890625 8.35571289 9.8132440549 22 23.890625 3.57446289 9.8132440550 23 23.890625 0.79321289 9.8132440551 24 23.890625 0.01196289 9.8132440552 25 23.890625 1.23071289 9.8132440553 26 23.890625 4.44946289 9.8132440554 21 23.890625 8.35571289 9.8132440555 27 23.890625 9.66821289 9.8132440556 28 23.890625 16.8869629 9.8132440557 29 23.890625 26.1057129 9.8132440558 18 23.890625 34.6994629 9.8132440559 26 23.890625 4.44946289 9.8132440560 22 23.890625 3.57446289 9.8132440561 27 23.890625 9.66821289 9.8132440562 26 23.890625 4.44946289 9.8132440563 20 23.890625 15.1369629 9.8132440564 25 23.890625 1.23071289 9.81324405

N 64

Max 30

Min 18

m 8

Rango 12

Amplitud de intervalos 1.500000000

nivel de confianza 0.95

0.05

INTERVALOS

LM inf. LM sup.

1 18.00 19.502 19.50 21.003 21.00 22.504 22.50 24.005 24.00 25.506 25.50 27.007 27.00 28.508 28.50 30.00

Total

1-

1 2 3 4 5 6 7 80

2

4

6

8

10

12

14

16

Column K

1 2 3 4 5 6 7 80

2

4

6

8

10

12

14

16

Column K

Z(xlim inf) Z(xlim sup)

5 -1.88 -1.40 0.0158 0.046513 -1.40 -0.92 0.0465 0.1131

5 -0.92 -0.44 0.1131 0.229610 -0.44 0.03 0.2296 0.3936

8 0.03 0.51 0.3936 0.579315 0.51 0.99 0.5793 0.7486

4 0.99 1.47 0.7486 0.87294 1.47 1.95 0.8729 0.9463

64

Oi(Frecuencia observada en cada intervalo)

P(Z(xlim inf))

P(Z(xlim sup))

1 2 3 4 5 6 7 80

2

4

6

8

10

12

14

16

Column K

1 2 3 4 5 6 7 80

2

4

6

8

10

12

14

16

Column K

Ei=N*P (Ei-Oi)^2/Ei

0.0307 1.9648 4.688741370.0666 4.2624 17.9114240.1165 7.456 0.809004290.164 10.496 0.02343902

0.1857 11.8848 1.269829620.1693 10.8352 1.600852690.1243 7.9552 1.966463070.0734 4.6976 0.10359455

Err:522

El estadistico en tablas seriaX0.05,8-2-1 11.07

P=P(Z(xlim sup))-P(Z(xlim inf))

X02

El estadistico de prueba es menor que el estadistico en tabla, por tanto podemos afirmar que los datos siguen una distribucion

normal.

El estadistico de prueba es menor que el estadistico en tabla, por tanto podemos afirmar que los datos siguen una distribucion

normal.

n xi ri1 19.5418255 0.62352 19.3452696 0.7098 MEDIA 23.8906253 17.1831546 0.4039 DESVIACION 3.13260978224 18.559046 0.30205 17.9693783 0.93736 17.7728224 0.14517 18.7556019 0.21578 20.1314933 0.23929 19.5418255 0.2471

10 19.3452696 0.584311 20.3280492 0.027512 21.7039405 0.176513 24.2591673 0.560814 24.0626114 0.019615 25.045391 0.843116 23.2763878 0.113717 25.8316146 0.874518 25.6350587 0.458819 26.6178382 0.654920 24.8488351 0.051021 27.4040619 0.184322 27.2075059 0.898023 25.045391 0.466724 26.4212823 0.992225 25.8316146 0.498026 25.6350587 0.333327 26.6178382 0.278428 27.9937296 0.929429 27.4040619 0.811830 27.2075059 0.772531 25.045391 0.090232 26.4212823 0.866733 25.8316146 0.121634 25.6350587 0.207835 26.6178382 0.905936 24.8488351 0.8039

METODO DE CONVOLUCION DISTRIBUCION NORMAL

Segn mi tipo De Distribucion Demostrada anteriormente: DISTRIBUCION NORMAL

La Distribucion normal puede ser generada a traves del metodo de convolucion.

La variable aleatoria normal con media y desviacin estndar puede generarse usando el teorema del lmite central dandonos la siguiente funcion de densidad despues de los calculos matematicos realizados:




37 24.2591673 0.435338 24.0626114 0.647139 25.045391 0.717640 23.2763878 0.741241 22.6867201 0.749042 22.4901642 0.082443 23.4729437 0.529444 24.8488351 0.678445 24.2591673 0.058846 27.2075059 0.521647 28.1902855 0.341248 29.5661768 0.615749 28.9765091 0.372550 28.7799532 0.960851 26.6178382 0.152952 27.9937296 0.552953 27.4040619 0.686354 25.2542316 0.396155 24.0134724 0.968656 20.9791406 0.490257 19.4435476 1.000058 16.3109378 0.835359 13.6942873 0.780460 11.2496232 0.427561 9.91058605 0.309862 8.94009126 0.270663 8.0924439 0.592264 6.23744752 0.3647

METODO DE CONVOLUCION DISTRIBUCION NORMAL







ALGORITM. CONGRUNCIAL MULTIPLICPRUEBA. MEDIAPRUEBA. VARIANZAP.CHI-CUADRADOP.CORRIDA ARRIBA Y ABAJO MEDIADATOSDISTRIBUCIONVARIABLES ALEATORIAS

estrella simu

Documents