70109A2Ed01 - MTODOS ESTADSTICOS PARA LA ADMINISTRACIN DE...

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4.1.- Distribuciones k-dimensionales. Análisis marginal y condicionado 4.2.- Variables aleatorias independientes. Propiedades 4.3.-Agregación de variables aleatorias 4.4.-Teorema Central del Límite y sus aplicaciones TEMA 4: ANÁLISIS CONJUNTO DE VARIABLES ALEATORIAS Y DISTRIBUCIÓN DE AGREGADOS MÉTODOS ESTADÍSTICOS PARA LA ADMINISTRACIÓN DE EMPRESAS TEMA 4. COMPETENCIAS • Saber calcular e interpretar la covarianza y el coeficiente de correlación lineal. • Conocer las principales propiedades derivadas de la independencia de variables aleatorias. • Saber aplicar e interpretar el Teorema Central del Límite.
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TEMA 4: ANÁLISIS CONJUNTO DE VARIABLES ALEATORIAS Y DISTRIBUCIÓN DE AGREGADOS 4.1.- Distribuciones k-dimensionales. Análisis marginal y condicionado MÉTODOS ESTADÍSTICOS PARA LA ADMINISTRACIÓN DE EMPRESAS Y \ X 2 4 8 0,1 0,2 0,1 2 0,05 0,05 0,1 3 0,1 0,1 0,2 1 Distribución conjunta de dos variables aleatorias xrhombus Valores (x i , y j ) xrhombus Probabilidades conjuntas p ij
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Variable aleatoria bidimensional Observación conjunta de dos variables aleatorias unidimensionales X e Y CASO DISCRETO Probabilidad conjunta p ij =P(X=x i ,Y=y j ) Y\X x 1 ... x i ... x k y 1 p 11 p i1 p k1 ... y j p 1j p ij p kj ... y l p 1l p il p kl Variables bidimensionales discretas (X,Y) v. a. DISCRETA 1,2,...} j )/i, y , {(x j i = P:(x,y) R 2 P(x,y) = P(X=x, Y=y) [0,1] Función de probabilidad conjunta ij j i p ) y Y , x P(X = = = 0 p ij 1 p i j ij = ∑∑
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Y \ X 2 4 8 0,1 0,2 0,1 2 0,05 0,05 0,1 3 0,1 0,1 0,2 1 F:(x,y) R 2 F(x,y) = P(X x, Y y) [0,1] Función de distribución bidimensional Probabilidad acumulada: P(X 4,Y 1) = 0,3 ∑∑ = x x y y ij i j p y) F(x, Función de distribución Distribuciones marginales Y \ X 2 4 8 0,1 0,2 0,1 2 0,05 0,05 0,1 3 0,1 0,1 0,2 1 P(Y=2) = 0,20 Distribución marginal de Y Distribución marginal de X P(X=4) = 0,35
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Distribuciones marginales Y\X x 1 ... x i ... x k y 1 p 11 p i1 p k1 ...
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