132:@0.053974:0.966765:0.079386:0.966765:0.079386:0.950778:0.053974:0.950778:0.000000:0.000000:0.000000
M.5.3.15.Calcular e interpretar la media, la varianza y la desviación estándar de una variable aleatoria discreta. :@0.143847:0.940354:0.586646:0.940354:0.586646:0.930312:0.143847:0.930312:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.3.17. Juzgar la validez de las soluciones obtenidas en los problemas que involucren el trabajo con probabilidades y variables aleatorias discretas dentro del contexto del problema.:@0.143847:0.949155:0.880898:0.949155:0.880898:0.939113:0.143847:0.939113:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Media, varianza y desviación :@0.404235:0.127666:0.769403:0.127666:0.769403:0.083007:0.404235:0.083007:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
estándar :@0.404235:0.165385:0.521535:0.165385:0.521535:0.120726:0.404235:0.120726:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.199646:0.112146:0.307805:0.112146:0.307805:0.096673:0.199646:0.096673:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Explica con tus pala-:@0.199884:0.140773:0.333146:0.140773:0.333146:0.125710:0.199884:0.125710:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bras, ¿qué entiendes por ‘valor :@0.153341:0.156615:0.353000:0.156615:0.353000:0.141552:0.153341:0.141552:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
esperado’?:@0.153341:0.172457:0.220621:0.172457:0.220621:0.157394:0.153341:0.157394:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Desequilibrio cognitivo:@0.199646:0.223016:0.363493:0.223016:0.363493:0.207543:0.199646:0.207543:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 ¿Qué relación existe :@0.199884:0.251643:0.336310:0.251643:0.336310:0.236580:0.199884:0.236580:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
entre ‘valor esperado’, ‘varianza’ :@0.153341:0.267485:0.358403:0.267485:0.358403:0.252422:0.153341:0.252422:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y ‘desviación típica’?:@0.153341:0.283327:0.281869:0.283327:0.281869:0.268264:0.153341:0.268264:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Media o esperanza matemática  ( ) de una variable :@0.404236:0.204249:0.823252:0.204249:0.823252:0.186566:0.404236:0.186566:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
E X:@0.658493:0.204490:0.685371:0.204490:0.685371:0.186581:0.658493:0.186581:0.000000:0.000000:0.000000
aleatoria discreta:@0.404236:0.222354:0.543103:0.222354:0.543103:0.204671:0.404236:0.204671:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición :@0.404236:0.239524:0.491103:0.239524:0.491103:0.222578:0.404236:0.222578:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sea   una variable aleatoria discreta con distribución de :@0.484322:0.239061:0.895980:0.239061:0.895980:0.222564:0.484322:0.222564:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
X:@0.520887:0.239177:0.530847:0.239177:0.530847:0.222708:0.520887:0.222708:0.000000
probabilidad  , la media ( ) o esperanza  ( ) de una variable aleato-:@0.404255:0.256412:0.891828:0.256412:0.891828:0.239914:0.404255:0.239914:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.499098:0.256528:0.508365:0.256528:0.508365:0.240059:0.499098:0.240059:0.000000
i:@0.508260:0.259756:0.510473:0.259756:0.510473:0.250155:0.508260:0.250155:0.000000
µ:@0.588843:0.256528:0.598091:0.256528:0.598091:0.240059:0.588843:0.240059:0.000000
E X:@0.697018:0.256528:0.720887:0.256528:0.720887:0.240059:0.697018:0.240059:0.000000:0.000000:0.000000
ria discreta   es::@0.404244:0.273763:0.516539:0.273763:0.516539:0.257265:0.404244:0.257265:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
X:@0.485021:0.273879:0.494981:0.273879:0.494981:0.257410:0.485021:0.257410:0.000000
µ E X:@0.586955:0.308580:0.639164:0.308580:0.639164:0.292111:0.586955:0.292111:0.000000:0.000000:0.000000:0.000000:0.000000
 =  ( ) =     :@0.596203:0.308464:0.680777:0.308464:0.680777:0.291967:0.596203:0.291967:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x p:@0.680777:0.308580:0.701925:0.308580:0.701925:0.292111:0.680777:0.292111:0.000000:0.000000:0.000000
i:@0.688201:0.311809:0.690414:0.311809:0.690414:0.302207:0.688201:0.302207:0.000000
i:@0.701849:0.311809:0.704062:0.311809:0.704062:0.302207:0.701849:0.302207:0.000000
.:@0.706307:0.308464:0.709062:0.308464:0.709062:0.291967:0.706307:0.291967:0.000000
Varianza de una variable aleatoria discreta:@0.404236:0.344563:0.744304:0.344563:0.744304:0.326881:0.404236:0.326881:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición :@0.404236:0.361734:0.491103:0.361734:0.491103:0.344788:0.404236:0.344788:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sea   una variable aleatoria discreta con distribución de :@0.484322:0.361271:0.895980:0.361271:0.895980:0.344773:0.484322:0.344773:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
X:@0.520887:0.361387:0.530847:0.361387:0.530847:0.344918:0.520887:0.344918:0.000000
probabilidad  , y media ( ), la varianza indica qué tan alejados se :@0.404255:0.378622:0.895944:0.378622:0.895944:0.362124:0.404255:0.362124:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.501275:0.378737:0.510542:0.378737:0.510542:0.362269:0.501275:0.362269:0.000000
i:@0.510453:0.381966:0.512666:0.381966:0.512666:0.372365:0.510453:0.372365:0.000000
µ:@0.593780:0.378737:0.603027:0.378737:0.603027:0.362269:0.593780:0.362269:0.000000
encuentran los valores de la media y se define como::@0.404240:0.395972:0.777462:0.395972:0.777462:0.379475:0.404240:0.379475:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
σ:@0.587760:0.438260:0.598301:0.438260:0.598301:0.419261:0.587760:0.419261:0.000000
2:@0.598298:0.424321:0.603251:0.424321:0.603251:0.414703:0.598298:0.414703:0.000000
 =     :@0.603250:0.430674:0.643052:0.430674:0.643052:0.414176:0.603250:0.414176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
   x p:@0.622341:0.430790:0.671580:0.430790:0.671580:0.414321:0.622341:0.414321:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i:@0.650488:0.434018:0.652701:0.434018:0.652701:0.424417:0.650488:0.424417:0.000000
2 :@0.654947:0.424324:0.662315:0.424324:0.662315:0.414706:0.654947:0.414706:0.000000:0.000000
i :@0.671504:0.434018:0.678378:0.434018:0.678378:0.424417:0.671504:0.424417:0.000000:0.000000
– .:@0.678377:0.430674:0.708246:0.430674:0.708246:0.414176:0.678377:0.414176:0.000000:0.000000:0.000000
  2:@0.688876:0.424321:0.705492:0.424321:0.705492:0.414703:0.688876:0.414703:0.000000:0.000000:0.000000
µ:@0.691292:0.430790:0.700539:0.430790:0.700539:0.414321:0.691292:0.414321:0.000000
Desviación típica o estándar de una variable aleatoria discreta:@0.404236:0.466773:0.887590:0.466773:0.887590:0.449090:0.404236:0.449090:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición :@0.404236:0.483943:0.491103:0.483943:0.491103:0.466997:0.404236:0.466997:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. La desviación típica o estándar de una variable aleatoria :@0.484322:0.483481:0.895922:0.483481:0.895922:0.466983:0.484322:0.466983:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
discreta es la raíz cuadrada de la varianza.:@0.404236:0.500831:0.695560:0.500831:0.695560:0.484334:0.404236:0.484334:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
σ:@0.585393:0.543119:0.595934:0.543119:0.595934:0.524120:0.585393:0.524120:0.000000
 =       :@0.595929:0.535533:0.644015:0.535533:0.644015:0.519035:0.595929:0.519035:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
   x p:@0.631589:0.535649:0.672543:0.535649:0.672543:0.519180:0.631589:0.519180:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i:@0.651451:0.538877:0.653664:0.538877:0.653664:0.529276:0.651451:0.529276:0.000000
2 :@0.655910:0.529183:0.663278:0.529183:0.663278:0.519565:0.655910:0.519565:0.000000:0.000000
i :@0.672467:0.538877:0.679341:0.538877:0.679341:0.529276:0.672467:0.529276:0.000000:0.000000
– .:@0.679341:0.535533:0.710613:0.535533:0.710613:0.519035:0.679341:0.519035:0.000000:0.000000:0.000000
  2:@0.689839:0.529180:0.706456:0.529180:0.706456:0.519562:0.689839:0.519562:0.000000:0.000000:0.000000
µ:@0.692255:0.535649:0.701502:0.535649:0.701502:0.519180:0.692255:0.519180:0.000000
 :@0.404238:0.552884:0.408380:0.552884:0.408380:0.536386:0.404238:0.536386:0.000000
Ejercicio resuelto:@0.404238:0.570610:0.522216:0.570610:0.522216:0.553823:0.404238:0.553823:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Se lanzan al aire, varias veces, dos dados iguales y se define la variable :@0.404238:0.587585:0.896001:0.587585:0.896001:0.571087:0.404238:0.571087:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aleatoria discreta   = “suma de los puntos de las caras obtenidas”. El :@0.404238:0.604936:0.895918:0.604936:0.895918:0.588438:0.404238:0.588438:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
X:@0.529366:0.605052:0.539326:0.605052:0.539326:0.588583:0.529366:0.588583:0.000000
espacio muestral de este evento se detalla en la tabla.:@0.404238:0.622287:0.781660:0.622287:0.781660:0.605789:0.404238:0.605789:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∑:@0.661020:0.311912:0.676399:0.311912:0.676399:0.286090:0.661020:0.286090:0.000000
n:@0.666455:0.292545:0.671913:0.292545:0.671913:0.282944:0.666455:0.282944:0.000000
i:@0.661895:0.317607:0.664107:0.317607:0.664107:0.308005:0.661895:0.308005:0.000000
=1:@0.665230:0.317539:0.676485:0.317539:0.676485:0.307921:0.665230:0.307921:0.000000:0.000000
∑:@0.623019:0.434199:0.638398:0.434199:0.638398:0.408376:0.623019:0.408376:0.000000
n:@0.628454:0.414832:0.633912:0.414832:0.633912:0.405230:0.628454:0.405230:0.000000
i:@0.623894:0.439893:0.626106:0.439893:0.626106:0.430292:0.623894:0.430292:0.000000
=1:@0.627229:0.439825:0.638483:0.439825:0.638483:0.430207:0.627229:0.430207:0.000000:0.000000
∑:@0.623969:0.538555:0.639348:0.538555:0.639348:0.512732:0.623969:0.512732:0.000000
n:@0.629403:0.519188:0.634862:0.519188:0.634862:0.509586:0.629403:0.509586:0.000000
i:@0.624843:0.544249:0.627056:0.544249:0.627056:0.534648:0.624843:0.534648:0.000000
=1:@0.628179:0.544181:0.639433:0.544181:0.639433:0.534563:0.628179:0.534563:0.000000:0.000000
Determina::@0.404236:0.844707:0.483147:0.844707:0.483147:0.828209:0.404236:0.828209:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a):@0.404236:0.878122:0.418781:0.878122:0.418781:0.861407:0.404236:0.861407:0.000000:0.000000
  La media o esperanza matemática:@0.418781:0.877905:0.669806:0.877905:0.669806:0.861407:0.418781:0.861407:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b):@0.404236:0.895472:0.420246:0.895472:0.420246:0.878758:0.404236:0.878758:0.000000:0.000000
  La varianza:@0.420246:0.895256:0.506188:0.895256:0.506188:0.878758:0.420246:0.878758:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c):@0.404236:0.912823:0.418570:0.912823:0.418570:0.896109:0.404236:0.896109:0.000000:0.000000
  La desviación típica o estándar:@0.418570:0.912606:0.645607:0.912606:0.645607:0.896109:0.418570:0.896109:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.510786:0.661089:0.518544:0.661089:0.518544:0.646026:0.510786:0.646026:0.000000
2:@0.563029:0.661089:0.570786:0.661089:0.570786:0.646026:0.563029:0.646026:0.000000
3:@0.615271:0.661089:0.623028:0.661089:0.623028:0.646026:0.615271:0.646026:0.000000
4:@0.667514:0.661089:0.675271:0.661089:0.675271:0.646026:0.667514:0.646026:0.000000
5:@0.719756:0.661089:0.727513:0.661089:0.727513:0.646026:0.719756:0.646026:0.000000
6:@0.771998:0.661089:0.779755:0.661089:0.779755:0.646026:0.771998:0.646026:0.000000
1:@0.458579:0.685645:0.466336:0.685645:0.466336:0.670581:0.458579:0.670581:0.000000
2:@0.510822:0.685645:0.518579:0.685645:0.518579:0.670581:0.510822:0.670581:0.000000
3:@0.563064:0.685645:0.570821:0.685645:0.570821:0.670581:0.563064:0.670581:0.000000
4:@0.615306:0.685645:0.623064:0.685645:0.623064:0.670581:0.615306:0.670581:0.000000
5:@0.667549:0.685645:0.675306:0.685645:0.675306:0.670581:0.667549:0.670581:0.000000
6:@0.719791:0.685645:0.727548:0.685645:0.727548:0.670581:0.719791:0.670581:0.000000
7:@0.772033:0.685645:0.779791:0.685645:0.779791:0.670581:0.772033:0.670581:0.000000
2:@0.458614:0.710200:0.466372:0.710200:0.466372:0.695137:0.458614:0.695137:0.000000
3:@0.510857:0.710200:0.518614:0.710200:0.518614:0.695137:0.510857:0.695137:0.000000
4:@0.563099:0.710200:0.570856:0.710200:0.570856:0.695137:0.563099:0.695137:0.000000
5:@0.615342:0.710200:0.623099:0.710200:0.623099:0.695137:0.615342:0.695137:0.000000
6:@0.667584:0.710200:0.675341:0.710200:0.675341:0.695137:0.667584:0.695137:0.000000
7:@0.719826:0.710200:0.727583:0.710200:0.727583:0.695137:0.719826:0.695137:0.000000
8:@0.772069:0.710200:0.779826:0.710200:0.779826:0.695137:0.772069:0.695137:0.000000
3:@0.458650:0.734755:0.466407:0.734755:0.466407:0.719692:0.458650:0.719692:0.000000
4:@0.510892:0.734755:0.518649:0.734755:0.518649:0.719692:0.510892:0.719692:0.000000
5:@0.563134:0.734755:0.570892:0.734755:0.570892:0.719692:0.563134:0.719692:0.000000
6:@0.615377:0.734755:0.623134:0.734755:0.623134:0.719692:0.615377:0.719692:0.000000
7:@0.667619:0.734755:0.675376:0.734755:0.675376:0.719692:0.667619:0.719692:0.000000
8:@0.719861:0.734755:0.727619:0.734755:0.727619:0.719692:0.719861:0.719692:0.000000
9:@0.772104:0.734755:0.779861:0.734755:0.779861:0.719692:0.772104:0.719692:0.000000
4:@0.458685:0.759310:0.466442:0.759310:0.466442:0.744247:0.458685:0.744247:0.000000
5:@0.510927:0.759310:0.518684:0.759310:0.518684:0.744247:0.510927:0.744247:0.000000
6:@0.563170:0.759310:0.570927:0.759310:0.570927:0.744247:0.563170:0.744247:0.000000
7:@0.615412:0.759310:0.623169:0.759310:0.623169:0.744247:0.615412:0.744247:0.000000
8:@0.667654:0.759310:0.675411:0.759310:0.675411:0.744247:0.667654:0.744247:0.000000
9:@0.719897:0.759310:0.727654:0.759310:0.727654:0.744247:0.719897:0.744247:0.000000
10:@0.768252:0.759310:0.783766:0.759310:0.783766:0.744247:0.768252:0.744247:0.000000:0.000000
5:@0.458720:0.783865:0.466477:0.783865:0.466477:0.768802:0.458720:0.768802:0.000000
6:@0.510962:0.783865:0.518720:0.783865:0.518720:0.768802:0.510962:0.768802:0.000000
7:@0.563205:0.783865:0.570962:0.783865:0.570962:0.768802:0.563205:0.768802:0.000000
8:@0.615447:0.783865:0.623204:0.783865:0.623204:0.768802:0.615447:0.768802:0.000000
9:@0.667689:0.783865:0.675447:0.783865:0.675447:0.768802:0.667689:0.768802:0.000000
10:@0.716044:0.783865:0.731559:0.783865:0.731559:0.768802:0.716044:0.768802:0.000000:0.000000
11:@0.768287:0.783865:0.783801:0.783865:0.783801:0.768802:0.768287:0.768802:0.000000:0.000000
6:@0.458755:0.808420:0.466512:0.808420:0.466512:0.793357:0.458755:0.793357:0.000000
7:@0.510998:0.808420:0.518755:0.808420:0.518755:0.793357:0.510998:0.793357:0.000000
8:@0.563240:0.808420:0.570997:0.808420:0.570997:0.793357:0.563240:0.793357:0.000000
9:@0.615482:0.808420:0.623239:0.808420:0.623239:0.793357:0.615482:0.793357:0.000000
10:@0.663837:0.808420:0.679352:0.808420:0.679352:0.793357:0.663837:0.793357:0.000000:0.000000
11:@0.716080:0.808420:0.731594:0.808420:0.731594:0.793357:0.716080:0.793357:0.000000:0.000000
12:@0.768322:0.808420:0.783836:0.808420:0.783836:0.793357:0.768322:0.793357:0.000000:0.000000
Segundo dado:@0.420708:0.768696:0.420708:0.704031:0.402549:0.704031:0.402549:0.768696:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Primer dado :@0.812715:0.661001:0.889009:0.661001:0.889009:0.647373:0.812715:0.647373:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Suma de :@0.827277:0.740670:0.882040:0.740670:0.882040:0.727042:0.827277:0.727042:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
puntos:@0.827277:0.755004:0.869021:0.755004:0.869021:0.741375:0.827277:0.741375:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.199644:0.366543:0.297267:0.366543:0.297267:0.351070:0.199644:0.351070:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.199644:0.379111:0.283707:0.379111:0.283707:0.363638:0.199644:0.363638:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La esperanza matemática :@0.199880:0.403585:0.365272:0.403585:0.365272:0.388522:0.199880:0.388522:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tiene algunas propiedades que :@0.153337:0.419427:0.352315:0.419427:0.352315:0.404364:0.153337:0.404364:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
enunciamos a continuación::@0.153337:0.435269:0.334075:0.435269:0.334075:0.420206:0.153337:0.420206:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.153337:0.458438:0.164542:0.458438:0.164542:0.443177:0.153337:0.443177:0.000000:0.000000
 La esperanza de una constan-:@0.164542:0.458240:0.360315:0.458240:0.360315:0.443177:0.164542:0.443177:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
te es el valor de la constante.:@0.170083:0.474082:0.355427:0.474082:0.355427:0.459019:0.170083:0.459019:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
E c:@0.231806:0.497159:0.251067:0.497159:0.251067:0.482122:0.231806:0.482122:0.000000:0.000000:0.000000
( ) =  .:@0.239071:0.497053:0.283011:0.497053:0.283011:0.481990:0.239071:0.481990:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.273934:0.497159:0.280495:0.497159:0.280495:0.482122:0.273934:0.482122:0.000000
2.:@0.153337:0.520222:0.164542:0.520222:0.164542:0.504961:0.153337:0.504961:0.000000:0.000000
 La esperanza de la suma de :@0.164542:0.520024:0.348513:0.520024:0.348513:0.504961:0.164542:0.504961:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dos variables aleatorias  inde-:@0.170083:0.535866:0.358613:0.535866:0.358613:0.520803:0.170083:0.520803:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
pendientes es igual a la suma :@0.170083:0.551708:0.360899:0.551708:0.360899:0.536645:0.170083:0.536645:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de las esperanzas de los dos :@0.170083:0.567550:0.353473:0.567550:0.353473:0.552487:0.170083:0.552487:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sumandos.:@0.170083:0.583392:0.239950:0.583392:0.239950:0.568329:0.170083:0.568329:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
E X Y:@0.184612:0.606469:0.233090:0.606469:0.233090:0.591432:0.184612:0.591432:0.000000:0.000000:0.000000:0.000000:0.000000
(  +  ) =  ( ) +  (Y).:@0.191877:0.606363:0.330203:0.606363:0.330203:0.591300:0.191877:0.591300:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
E X:@0.255957:0.606469:0.277751:0.606469:0.277751:0.591432:0.255957:0.591432:0.000000:0.000000:0.000000
E:@0.300618:0.606469:0.307883:0.606469:0.307883:0.591432:0.300618:0.591432:0.000000
3.:@0.153337:0.629532:0.164542:0.629532:0.164542:0.614271:0.153337:0.614271:0.000000:0.000000
 La esperanza del producto :@0.164542:0.629334:0.344168:0.629334:0.344168:0.614271:0.164542:0.614271:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de dos variables aleatorias :@0.170083:0.645176:0.341234:0.645176:0.341234:0.630113:0.170083:0.630113:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
independientes es igual al :@0.170083:0.661018:0.339579:0.661018:0.339579:0.645955:0.170083:0.645955:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
producto de las esperanzas :@0.170083:0.676860:0.350131:0.676860:0.350131:0.661797:0.170083:0.661797:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de los dos factores.:@0.170083:0.692702:0.293104:0.692702:0.293104:0.677639:0.170083:0.677639:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
E X Y:@0.198104:0.715778:0.232932:0.715778:0.232932:0.700742:0.198104:0.700742:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.205368:0.715673:0.210804:0.715673:0.210804:0.700610:0.205368:0.700610:0.000000
) =  ( )  ( ).:@0.232932:0.715673:0.316713:0.715673:0.316713:0.700610:0.232932:0.700610:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
E X E Y:@0.255799:0.715778:0.308763:0.715778:0.308763:0.700742:0.255799:0.700742:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000