186:@0.067867:0.963104:0.109245:0.963104:0.109245:0.941283:0.067867:0.941283:0.000000:0.000000:0.000000
Matemática:@0.120102:0.956142:0.204868:0.956142:0.204868:0.943479:0.120102:0.943479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.º BG:@0.120102:0.967458:0.162238:0.967458:0.162238:0.954794:0.120102:0.954794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
isposición y compromiso:@0.306727:0.140863:0.485691:0.140863:0.485691:0.125499:0.306727:0.125499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
D:@0.284763:0.141649:0.297589:0.141649:0.297589:0.124513:0.284763:0.124513:0.000000
¿Qué es un promedio?:@0.093595:0.192000:0.244164:0.192000:0.244164:0.177101:0.093595:0.177101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.108521:0.163125:0.227756:0.163125:0.227756:0.146224:0.108521:0.146224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Media o esperanza matemática  ( ) de una variable aleatoria :@0.287495:0.544937:0.905599:0.544937:0.905599:0.523427:0.287495:0.523427:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
E X:@0.607137:0.544937:0.638658:0.544937:0.638658:0.525011:0.607137:0.525011:0.000000:0.000000:0.000000
discreta :@0.287495:0.566060:0.372678:0.566060:0.372678:0.544550:0.287495:0.544550:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sea   una variable aleatoria discreta con distribución de probabilidad  , la media ( ) :@0.287495:0.588841:0.907692:0.588841:0.907692:0.572452:0.287495:0.572452:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
X:@0.317680:0.588841:0.326746:0.588841:0.326746:0.572479:0.317680:0.572479:0.000000
p:@0.798693:0.588841:0.807962:0.588841:0.807962:0.572479:0.798693:0.572479:0.000000
i:@0.807914:0.592004:0.810127:0.592004:0.810127:0.582466:0.807914:0.582466:0.000000
μ:@0.889467:0.588841:0.898773:0.588841:0.898773:0.572479:0.889467:0.572479:0.000000
o esperanza  ( ) de una variable aleatoria es::@0.287500:0.605437:0.613150:0.605437:0.613150:0.589048:0.287500:0.589048:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
E X:@0.379768:0.605437:0.401844:0.605437:0.401844:0.589076:0.379768:0.589076:0.000000:0.000000:0.000000
n:@0.616556:0.619656:0.622100:0.619656:0.622100:0.610118:0.616556:0.610118:0.000000
i:@0.610046:0.645692:0.612259:0.645692:0.612259:0.636153:0.610046:0.636153:0.000000
 = 1:@0.612259:0.645692:0.628610:0.645692:0.628610:0.636137:0.612259:0.636137:0.000000:0.000000:0.000000:0.000000
μ E X:@0.537228:0.637864:0.586928:0.637864:0.586928:0.621503:0.537228:0.621503:0.000000:0.000000:0.000000:0.000000:0.000000
 =  ( ) = :@0.546534:0.637864:0.610497:0.637864:0.610497:0.621475:0.546534:0.621475:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∑:@0.610142:0.640064:0.624766:0.640064:0.624766:0.613246:0.610142:0.613246:0.000000
 x p:@0.624766:0.637864:0.648488:0.637864:0.648488:0.621503:0.624766:0.621503:0.000000:0.000000:0.000000:0.000000
i  i:@0.635247:0.641028:0.650701:0.641028:0.650701:0.631489:0.635247:0.631489:0.000000:0.000000:0.000000:0.000000
.:@0.650701:0.637864:0.653907:0.637864:0.653907:0.621475:0.650701:0.621475:0.000000
Varianza de una variable aleatoria discreta:@0.287495:0.682411:0.714973:0.682411:0.714973:0.660902:0.287495:0.660902:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sea   una variable aleatoria discreta con distribución de probabilidad  , y media ( ), :@0.287495:0.705192:0.907683:0.705192:0.907683:0.688804:0.287495:0.688804:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
X:@0.317754:0.705192:0.326820:0.705192:0.326820:0.688831:0.317754:0.688831:0.000000
p:@0.799397:0.705192:0.808666:0.705192:0.808666:0.688831:0.799397:0.688831:0.000000
i:@0.808651:0.708356:0.810864:0.708356:0.810864:0.698818:0.808651:0.698818:0.000000
μ:@0.886251:0.705192:0.895557:0.705192:0.895557:0.688831:0.886251:0.688831:0.000000
la varianza indica qué tan alejados se encuentran los valores de la media y se define :@0.287500:0.721789:0.907775:0.721789:0.907775:0.705400:0.287500:0.705400:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como::@0.287500:0.738385:0.333625:0.738385:0.333625:0.721996:0.287500:0.721996:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.578721:0.752604:0.584264:0.752604:0.584264:0.743066:0.578721:0.743066:0.000000
i:@0.572210:0.778640:0.574423:0.778640:0.574423:0.769101:0.572210:0.769101:0.000000
 = 1:@0.574423:0.778640:0.590775:0.778640:0.590775:0.769085:0.574423:0.769085:0.000000:0.000000:0.000000:0.000000
σ:@0.539758:0.770812:0.549138:0.770812:0.549138:0.754451:0.539758:0.754451:0.000000
2:@0.549138:0.764765:0.554380:0.764765:0.554380:0.755210:0.549138:0.755210:0.000000
 = :@0.554380:0.770812:0.573434:0.770812:0.573434:0.754423:0.554380:0.754423:0.000000:0.000000:0.000000
∑:@0.573434:0.773013:0.588059:0.773013:0.588059:0.746194:0.573434:0.746194:0.000000
 x p – μ:@0.588057:0.770812:0.642929:0.770812:0.642929:0.754451:0.588057:0.754451:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i:@0.598837:0.773976:0.601050:0.773976:0.601050:0.764437:0.598837:0.764437:0.000000
2:@0.601050:0.764768:0.606293:0.764768:0.606293:0.755213:0.601050:0.755213:0.000000
i:@0.615563:0.773976:0.617776:0.773976:0.617776:0.764437:0.615563:0.764437:0.000000
2:@0.642929:0.764765:0.648172:0.764765:0.648172:0.755210:0.642929:0.755210:0.000000
.:@0.648171:0.770812:0.651378:0.770812:0.651378:0.754423:0.648171:0.754423:0.000000
Desviación típica o estándar de una variable aleatoria :@0.287495:0.815360:0.831815:0.815360:0.831815:0.793850:0.287495:0.793850:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
discreta:@0.287495:0.836482:0.367823:0.836482:0.367823:0.814972:0.287495:0.814972:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La desviación típica o estándar de una variable aleatoria discreta es la raíz cuadrada :@0.287495:0.859265:0.907678:0.859265:0.907678:0.842876:0.287495:0.842876:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la varianza.:@0.287495:0.875861:0.390154:0.875861:0.390154:0.859472:0.287495:0.859472:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.575310:0.890080:0.580854:0.890080:0.580854:0.880542:0.575310:0.880542:0.000000
i:@0.568799:0.916116:0.571013:0.916116:0.571013:0.906577:0.568799:0.906577:0.000000
 = 1:@0.571013:0.916116:0.587364:0.916116:0.587364:0.906561:0.571013:0.906561:0.000000:0.000000:0.000000:0.000000
σ:@0.533704:0.908288:0.543083:0.908288:0.543083:0.891927:0.533704:0.891927:0.000000
 =   :@0.543083:0.908288:0.570209:0.908288:0.570209:0.891899:0.543083:0.891899:0.000000:0.000000:0.000000:0.000000:0.000000
∑:@0.570209:0.910488:0.584834:0.910488:0.584834:0.883670:0.570209:0.883670:0.000000
 x p – μ:@0.584832:0.908288:0.639705:0.908288:0.639705:0.891927:0.584832:0.891927:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i:@0.595612:0.911452:0.597825:0.911452:0.597825:0.901913:0.595612:0.901913:0.000000
2:@0.597825:0.902244:0.603068:0.902244:0.603068:0.892689:0.597825:0.892689:0.000000
i:@0.612338:0.911452:0.614551:0.911452:0.614551:0.901913:0.612338:0.901913:0.000000
2:@0.639705:0.902241:0.644947:0.902241:0.644947:0.892686:0.639705:0.892686:0.000000
.:@0.644946:0.908288:0.648153:0.908288:0.648153:0.891899:0.644946:0.891899:0.000000
nidad de conocimientos:@0.306727:0.513809:0.480398:0.513809:0.480398:0.498444:0.306727:0.498444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U:@0.284892:0.514594:0.297460:0.514594:0.297460:0.497459:0.284892:0.497459:0.000000
Pienso y progreso:@0.294883:0.461563:0.417347:0.461563:0.417347:0.446199:0.294883:0.446199:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Piensa en situaciones en las que debes tomar una decisión que no solo dependa de ti.:@0.294883:0.480214:0.868011:0.480214:0.868011:0.465315:0.294883:0.465315:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En algunas circunstancias de la vida cotidiana nos enfrentamos a situaciones con :@0.287495:0.168345:0.907751:0.168345:0.907751:0.151956:0.287495:0.151956:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
resultados inciertos, como calcular gastos, evaluar riesgos o planificar presupuestos. :@0.287495:0.184941:0.907639:0.184941:0.907639:0.168553:0.287495:0.168553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La esperanza matemática, la varianza y la desviación estándar son herramientas esta-:@0.287495:0.201538:0.903714:0.201538:0.903714:0.185149:0.287495:0.185149:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dísticas que nos ayudan a examinar estas situaciones. :@0.287495:0.218134:0.681287:0.218134:0.681287:0.201745:0.287495:0.201745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A continuación, tenemos un problema práctico donde aplicaremos estos conceptos :@0.287495:0.241853:0.907696:0.241853:0.907696:0.225464:0.287495:0.225464:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a una variable aleatoria discreta. :@0.287495:0.258450:0.524711:0.258450:0.524711:0.242061:0.287495:0.242061:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Andrés usa tres medios de transporte para ir al trabajo: autobús, taxi o bicicleta. Cada :@0.287495:0.282169:0.907604:0.282169:0.907604:0.265780:0.287495:0.265780:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
opción tiene un costo diferente y una probabilidad de uso que depende del clima: :@0.287495:0.298765:0.895530:0.298765:0.895530:0.282376:0.287495:0.282376:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Transporte:@0.304060:0.326165:0.382930:0.326165:0.382930:0.310801:0.304060:0.310801:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Costo en dólares (   ):@0.411276:0.326165:0.561943:0.326165:0.561943:0.310801:0.411276:0.310801:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.543098:0.326165:0.551006:0.326165:0.551006:0.311933:0.543098:0.311933:0.000000
i:@0.551002:0.329041:0.553434:0.329041:0.553434:0.320744:0.551002:0.320744:0.000000
Probabilidad :@0.607543:0.326165:0.704406:0.326165:0.704406:0.310801:0.607543:0.310801:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.704406:0.326165:0.713368:0.326165:0.713368:0.311933:0.704406:0.311933:0.000000
i:@0.713370:0.329041:0.715802:0.329041:0.715802:0.320744:0.713370:0.320744:0.000000
Condición climática:@0.755150:0.326165:0.897025:0.326165:0.897025:0.310801:0.755150:0.310801:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Autobús:@0.315048:0.348432:0.371956:0.348432:0.371956:0.333533:0.315048:0.333533:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5 :@0.482522:0.348432:0.494366:0.348432:0.494366:0.333533:0.482522:0.333533:0.000000:0.000000
0,5:@0.652039:0.348432:0.671305:0.348432:0.671305:0.333533:0.652039:0.333533:0.000000:0.000000:0.000000
Día normal:@0.789359:0.348432:0.862801:0.348432:0.862801:0.333533:0.789359:0.333533:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Taxi:@0.330963:0.367392:0.356008:0.367392:0.356008:0.352493:0.330963:0.352493:0.000000:0.000000:0.000000:0.000000
20:@0.478417:0.367392:0.494768:0.367392:0.494768:0.352493:0.478417:0.352493:0.000000:0.000000
0,3:@0.652023:0.367392:0.671288:0.367392:0.671288:0.352493:0.652023:0.352493:0.000000:0.000000:0.000000
Lluvia:@0.806748:0.367392:0.845379:0.367392:0.845379:0.352493:0.806748:0.352493:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Bicicleta:@0.316036:0.386352:0.370901:0.386352:0.370901:0.371453:0.316036:0.371453:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.482488:0.386352:0.490663:0.386352:0.490663:0.371453:0.482488:0.371453:0.000000
0,2:@0.652006:0.386352:0.671271:0.386352:0.671271:0.371453:0.652006:0.371453:0.000000:0.000000:0.000000
Día soleado:@0.787013:0.386352:0.865096:0.386352:0.865096:0.371453:0.787013:0.371453:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a):@0.287495:0.415466:0.302403:0.415466:0.302403:0.398566:0.287495:0.398566:0.000000:0.000000
  Calcula la esperanza matemática (gasto esperado por semana) de Andrés.:@0.302403:0.415466:0.855098:0.415466:0.855098:0.399077:0.302403:0.399077:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b):@0.287495:0.435631:0.303712:0.435631:0.303712:0.418730:0.287495:0.418730:0.000000:0.000000
  Determina la varianza y la desviación estándar del gasto semanal.:@0.303712:0.435631:0.792995:0.435631:0.792995:0.419242:0.303712:0.419242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Media, varianza y desviación estándar:@0.286308:0.075160:0.845734:0.075160:0.845734:0.041608:0.286308:0.041608:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.094760:0.108603:0.159692:0.108603:0.159692:0.011514:0.094760:0.011514:0.000000
©Shutterstock:@0.070380:0.355858:0.070380:0.313032:0.058469:0.313032:0.058469:0.355858:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En muchas ocasiones, el :@0.072616:0.411251:0.220928:0.411251:0.220928:0.397841:0.072616:0.397841:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
medio de transporte que :@0.072616:0.423822:0.226581:0.423822:0.226581:0.410413:0.072616:0.410413:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
escogemos está sujeto a :@0.072616:0.436394:0.223052:0.436394:0.223052:0.422985:0.072616:0.422985:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
condiciones como nuestro :@0.072616:0.448966:0.236714:0.448966:0.236714:0.435557:0.072616:0.435557:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
presupuesto o el clima.:@0.072616:0.461538:0.211339:0.461538:0.211339:0.448128:0.072616:0.448128:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Como estudiante, elige :@0.089232:0.604554:0.247239:0.604554:0.247239:0.589655:0.089232:0.589655:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
rutas seguras para ir a tu :@0.081660:0.619642:0.247241:0.619642:0.247241:0.604743:0.081660:0.604743:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
institución, cruza siempre :@0.073585:0.634730:0.247239:0.634730:0.247239:0.619831:0.073585:0.619831:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por los pasos peatonales y :@0.067973:0.649817:0.247239:0.649817:0.247239:0.634918:0.067973:0.634918:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
evita el uso del celular o :@0.083603:0.664905:0.247241:0.664905:0.247241:0.650006:0.083603:0.650006:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
audífonos al caminar :@0.104946:0.679992:0.247241:0.679992:0.247241:0.665093:0.104946:0.665093:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cerca del tránsito. Si :@0.112015:0.695080:0.247239:0.695080:0.247239:0.680181:0.112015:0.680181:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
puedes, usa la bicicleta o :@0.077941:0.710168:0.247239:0.710168:0.247239:0.695269:0.077941:0.695269:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
camina: es saludable, :@0.103371:0.725255:0.247237:0.725255:0.247237:0.710356:0.103371:0.710356:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ecológico y económico.:@0.084407:0.740343:0.243570:0.740343:0.243570:0.725444:0.084407:0.725444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué medio de transporte :@0.079767:0.852883:0.246584:0.852883:0.246584:0.838009:0.079767:0.838009:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
usas para ir a tu colegio? :@0.088328:0.867970:0.246586:0.867970:0.246586:0.853096:0.088328:0.853096:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cómo crees que puedes :@0.088814:0.883058:0.246588:0.883058:0.246588:0.868184:0.088814:0.868184:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ayudar al medioambiente?:@0.072513:0.898145:0.243569:0.898145:0.243569:0.883272:0.072513:0.883272:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Seguridad vial:@0.129537:0.569262:0.238093:0.569262:0.238093:0.552361:0.129537:0.552361:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
©Shutterstock:@0.065631:0.808344:0.065631:0.765519:0.053720:0.765519:0.053720:0.808344:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.3.15. :@0.298180:0.945471:0.353423:0.945471:0.353423:0.933179:0.298180:0.933179:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Calcular e interpretar la media, la varianza y la desviación estándar de una variable aleatoria discreta.:@0.353423:0.945471:0.883916:0.945471:0.883916:0.933552:0.353423:0.933552:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000