Variaveis Aleatorias Discretas



Ω.



Ω 





Ω



Ω

Ω 











( )≥ ( ≤

´  +

∞

−∞

≤ )= ( )

=

´ 

( )

( )=

−

( )= = ´  ( ≤ ≤ )= −









≤

≤ ≤ ≤ = | =

−

=





( ) = =



( = )+ ( = )

(

=

) + ... +

(

=

)=

=

× (

( )= 

=

)

=



σ



σ



( )=σ

 = (

− µ)

( )



  ( − µ) ( ) = (  − ( ) = σ =  ( )− µ ( )+µ ( ) =

µ + µ

) ( )= ( )−µ

( ) × = × = × = × = ( )= (

)−µ =

,

( )= , − , =.

( ( (

+

) = ( )+ ( )

)= ( ) ( )

)=

,

( )

( ( (

+ −

)= )=

− )

=µ= ( )

( )+ ( )+

( ) ( )

(

= )  ( )= ( )= ( )= , ( )= ( ) = ( )−µ = (

(

+ )= , + ( + )= +

)

=

,

(

− (

( − )= , +

)=

−

,

)= , − × = (

)

= , ,

,

=



(

,

(

+

) = [(

− µ )(

− µ )] = (

)− ( ) ( )





)=

( )+

( )+

(

,

)

( )

×

+

)× (

×

=

×

=

×

=

×

=

×

=

×

=

×

=

×

=

×

=

×

=

×

=

×

=

×

=

×

=

×

=

×

=

×

=

×

=

×

=

×

=

×

=

×

=

×

=

( )=

)

)=



+

(

=

× (

( )+ ( ) =

( )

×

( )=

(

×

=

( + )= = ( + )

(

+

)=

+

)



(

,

)= (

)− ( )× ( )=

−

×

=



( )

( )

(

+

)

(

×

=

×

=

×

=

×

=

×

=

×

=

×

=

×

=

×

=

×

=

×

=

×

=

×

=

×

=

×

=

×

=

×

=

×

=

(

)=

(

)=

((

+

+

)

) )=



( +

) = (( +

) )− ( +

) =

−( ) =



( (

+ )= ( )+ ( )+ )− ( ) + ( )− ( ) +

(

)= ( , )=

,

,





(

+ )= ( + + )= ( + )= ( )= ( )= ×( −( ) )= , ( , )= ( , + ) = ( ( + )) − ( ) ( + ) = ( + ) − ( )( ( ) + ) = × + × − ( × + )=