STATISTIKA_THEORY WEEK 5 Distribusi Probabilitas Diskrit

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  ! !

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  8 B ? /

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  ' & " # ' * # ; # $ (B7 & )+ ! $ $ # ' ( )

  ! . ;> # $ $ * * +

  0B # $ $ ! ! " + ! B # # # # $ ! # $ $ ! $

• ! 9>/0 + 2 # # " " '# 0' ! " # ! " #& ' $$ B ' ! # ! " #

  "

  0B # ! " # # & "! '  

  # $ " $ ! $ '  

  B  

   

  B − B

  ( ) " # ! ! '

  9  

  B    

  ' !! " $' !# # # $ ! # $ $ ! $ ! 9>/0 & " #

  ! ' * # " ! ; # # # ! " 0 ' ! '

  = B B

• $ ! ! / . >3

  (B7 & )

  9

  7 B & & & B −

    = =    

  # * $ " ' $ * $ $ ! ?+C@+ $ ! '- 1 =

  # * $ $ # # #+ < - .

  ! $ ! $

  D D D ( 7 & ) ( ) ( )  

  = = =    

  ! $ " ' # $ ! ' ! ' ?+=+ 2 ! # ' /@ $ " # & ! $.

  )+ # $0# $ /? $ " ' )+ 3 " E $ $ " '

• )+ @ $ $ " ' < - .

  . ; > " # # $ $ " ' , # , # . . > ?+= > ?+= > /@ > /@

• (; ≥ ) = − (; < ) = − (; = ) (; = + ) (; = )

  )+

  [ ]

  = − (B7 7 + ) ← ! ' ! ∑

  B = = − +

  ) < ! 3 " E $ $ " ' > ?+ECCF

  B B ( ; ) (; ) (; ) (B7 & + ) (B7 & + ) ! ' !

  ≤ ≤ = ≤ − ≤

= − ←

= − =

  ∑ ∑

• = =

  (; ) ( 7 7 + ) (; ) (; ) = = = ≤ − ≤

• )
• )

  B B (; ) ( 7 7 + ) (; ) (; ) (B7 & + ) (B7 & + ) ! ' !

  ?+=?31 0 ?+1/C3 ?+/E@F = =

  = = = ≤ − ≤ = − ← = =

  ∑ ∑

  ! 3 " $$ # ! " !

• " & ! $# ' . #
• ! " ! 2 " !. $ " $$ #

  ! ' _{I/J ?+FKK/KKC H "(F&/@&?+=)} $ # % - G & ! $# ' (G * "" ).

  H "(E&/@&?+=) _{H "(1&/@&?+=) I/J ?+F?=F@1K I/J ?+=?31/@K H "(@&/@&?+=)} I/J ?+?1C//= I/J ?+?1C//= _{I/J ?+1/C1CCC} H "(=&/@&?+=)

  , 2 " ! (B7 & ) " "

  5

  # " 5 * ' 1

   !

  , * ' @+K # ' >/@ >?+= = ( )( + ) = , ! '.

  σ σ = = ( )( + )( + ) ( )( + )( + ) = = + +

  , ,

  σ = +

  " /+ % # # ( ) 1+ 2 # # ! ' !

  ≠ 9 3+ 2 # " ! > 9 ! #

• /+ " " ! # ' ! # . # $ $ ! $ $ !
• 1+ ! #

  ' ! ' " # $ 3+

  ' % ( ) *

• =+ < "! ' $ " # # "

  $ $ - , $

  $ ( % 5 ) ! ' # " $# $ 5 ! " # + , $$ $

  " ! ! ( # ) * # ! ' & $# ! # # * !+

  $ # # " # * # # . # $ ! " * # $ $#

  7 "! ' ! ' * # ! " ' ! " # #7

  "! ' ! ' " $ # " ! " 7 # " # " ! ! $+

  ! $ $ " $ # ! , ! ' # " & # ! '

• # # & ! # ! $$ , , " # " # ! ' ! ' '! '!
• " " #

  "L ' /E3C& $$

  " ! ' " $ # #

  $ " $' !# ' * # ; $ " # * # ' ! ! " ! " ! $ - # ' 8 6+

  " " ! # % 0 % # . /+ 2 # # # $ ! " ' ( ! $)

• #
• $ ' ! 1+ ! # ! " ' ! $ $ # * ! #

  $ $ # # $ ! ! $+ 3+ ! $ ! ' # ! " ' $

  " + #

  , ' * # ; $ " # # # # $ ! " ! $ - # ' & # .

  " . >1&C/E1E " # # # $ - # +

  !# & # ! ?&/ " /E

  B ( ) BD

  (B& )

  7B & & &+++++

  λ λ λ

  −

  = =

  λ λ =

  # ! + G # # " # $ '

  ! ' ! ' /?+ ! ' ' " " " " $

   !

  !# . ; > # # " # $ ' ; > M/& 1& 3& + + + + + & /@N

  # (; > ) = − (; ≤ ) = − (B7 ) ← !

  ∑ B =

  = − = + + < ! $ ' # # $ > ?+?=EC

  !# ' " ! #! # # # !+ # $ " " #! # " !# " " /?? " * + < # # " $# $ # " " ! # ! ?&????1 , # .

• 2 $# ' '
• # # " "
• 2 # " $# '- $ # " " ! #! ' $
• 2 # " $# # $ " " ! < - < - . . , # ' > /??+??? > ?&????1 + 2 $ ' # # " " ! .

• + " $# '- $ " " ! #! ' $

  ; > / #

  

≈ = = =

−

  ≈ = = = −

• " $# # $ " " ! ; > ?
• " $# # $ " " ! ; > ?

  ! ! '- $ # " # #

  2 ! ' ?&??/+ , 1??? $ #

  ! $ $ # " +

• $ " # ! ' $

  ' *+ 1 $ $ " < - < - . .

  , # ' > 1??? > ?&??/ > + > 1??? ; ?&??/ > 1

• $ $ # "
• $ " # ! ' $

  ≈ = = = = −

• ' $ D
• − −

  = = = = =

  , " "

  5

  λ = $

  G # # ! % $ " ! $' $ ! " / " ! # ! " * ! " ! ' =+ ! K # ! " ! - ' $ ! " / " ! # + < - .

  (B& ) λ

  σ λ = < - .

  ! $ ! '

  B = 7 λ = =

  ( ) D B B

  ( 7 ) (B7 ) (B7 ) & & &

  − = =

  = = − = − =

  ∑ ∑

  ! = " $$ # ! $$ # G. H (K&=) I/J ?+EEF31K H (@&=) I/J ?+CE@/3?=

  ! # >/@& >?+=& " $$ # ! ! '.

  !# ; ' * # " ! $ ! (B& & )+ < # &

  " " # → ∞ → =

  (B& & ) → (B& ) , ! " # $ " $' !# $ $ ! &

• $ ! " $ ! " $(* * ) $(* * ) $ # $ # $ "
• $ " # # ! ! # # < # # ' / /??? $ $ ' !# " "

  ! ' $ ! " $+ 2 ! '- ! " " !

• # E??? $ # # $ C $ $ ! " $O

   !

  

< # # " $$ # !& * ! & $ # G& ! $# '

H "(K&E???&?+??/) I/J ?+3/31@1/ H (K&E)

  B

  =

  =

  (B7 ) ?+3/33C=3

  ∑ B

  =

  =

  (B7 & + ) ?+3/31@1/

  ,

  I/J ?+3/33C=3 , ! '.

  ∑

  (B7 & + ) ?+3/31@1/ =

  ∑ ∑

  < = = =

  = =

  (; ) (B7 & + ) (B7 ) &

  B B

  ∑

  " # $ $ $ % $ & $ ' ' $

  

( ) & $ % # * ) # ) + ) , $

# # & & # ) & # ) & # # # # & # & #

$ % # $ % # * ) * ) # # + ) , $ + ) , $ # # & &

  ) # %

' ' ) * ) ) ' & # $ % # # )

) , $

  # $ # & ' # ) & $ * ) # #