# 3885186-Formulario-Probabilidades - PERMUTACIONES n n = n...

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PERMUTACIONES ! n n n = & )! ( ! r n n r n ± = & definición )! 1 ( ± = & nn n C permutación circular ! !... ! ! ... 2 1 2 1 k k n n n n n n n n = & distinguibles. COMBINACIONES )! ( ! ! r n r n C nCr n r ± = = definición. PROBABILIDAD CONDICIONAL ) ( ) ( ) ( B P B A P B A P ² = Propiedades: ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( B A C P A B P A P C B A P A B P A P B A P B A P B P B A P ² ² ² ² ² ³ ³ = ³ = ³ = TEOREMA DE PROBABILIDAD TOTAL Sea B 1 , B 2 , …,B k . una partición, A un evento: ´ = = k i i i B A P B P A P 1 ) ( ) ( ) ( TEOREMA DE BAYES Sea B 1 , B 2 , …,B k . una partición, A un evento: ´ = = k i i i k k k B A P B P B A P B P A B P 1 ) ( ) ( ) ( ) ( ) ( EVENTOS INDEPENDIENTES i) ) ( ) ( ) ( BP A P B A P = ² ó ii) ) ( ) ( AP B A P = VARIABLES ALEATORIAS VARIABLES ALEATORIAS DISCRETAS FUNCION DE PROBABILIDAD. Una función p(x)=P[X = x]= ´ }) ({ w P , que satisface: i) p(x)>0, ii) ´ ´ = = ][ ) ( xX P x P =1 FUNCION DE DISTRIBUCION Sea p(x i ) una función de probabilidad: F(x) = ´ ´ µ µ = = = µ x X i x X i i i x X P x p x X P ) ( ] [ ESPERANZA MATEMATICA ) ( 1 ´ = = = n i i i x p x Ex VARIANZA DE UNA V.A.D. ) ( ) ( ) var( 2 2 i i x p x x ´ ± = = DESVIACION ESTANDAR 2 = LA MODA VARIABLES ALEATORIAS CONTINUAS. FUNCION DE DENSIDAD DE PROBABILIDAD · ¸ ¸ ± = ¹ 1 ) ( 0 ) ( dx x f x f FUNCION DE DISTRIBUCION ACUMULADA DE UNA VARIABLE ALEATORIA CONTINUA ) ( ) ( ) ( tx P t x P t F µ < ±¸ = µ = VALOR ESPERADO ·

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## This note was uploaded on 01/12/2011 for the course ADM D13 taught by Professor Lic.diaz during the Fall '10 term at Universidad Catolica Argentina.

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3885186-Formulario-Probabilidades - PERMUTACIONES n n = n...

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