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Descarga gou! y comparte coche por la city ahorrando pasta - Estadística (grado en ADE): Apuntes de apoyo (Grupo 7 Curso 2012/13) Tema 7 pág. 3 Dem : ( 1 2 1 2 1 2 ( , ) ( ) ( ) ( ) Cov X X Y Media X X Y Media X X Media Y = + - + = ( 1 2 1 2 ( ) ( ) ( ) ( ) ( ) Media X Y Media X Y Media X Media X Media Y = + - + , expresión que multiplicando y agrupando se convierte en 1 2 ( , ) ( , ) Cov X Y Cov X Y , y donde en esta demostración se ha aplicado la propiedad general ( ) ( ) ( ) Media X Y Media X Media Y = + que a su vez es fácil de demostrar. Por simetría también 1 2 1 2 ( , ) ( , ) ( , ) Cov X Y Y Cov X Y Cov X Y + = + y aplicando dos veces esta propiedad lineal 1 2 1 2 1 1 2 1 1 2 2 2 ( , ) ( , ) ( , ) ( , ) ( , ) Cov X X Y Y Cov X Y Cov X Y Cov X Y Cov X Y + + = + + + 6) ( , ) 0 Cov a Y = pues ( , ) ( ) 0 Cov a Y Media aY ay ay ay = - = - = . Análogamente ( , ) 0 Cov X b = 7) ( , ) ( , ) Cov X a Y Cov X Y = pues ( , ) ( , ) ( , ) Cov X a Y Cov X Y Cov a Y + = + 0 ( , ) Cov X Y = dncurlybracketlefthorizcurlybracketextdncurlybracketmidhorizcurlybracketextdncurlybracketright .

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