Bayes theorem

 

E A1, A2, A3 , ..., An S P(E) > 0   :

(Prior probability) ( ) ɡ (Posterior distribution) .

:

(1)                    (2)                    (3)                    (4)                    (5)

    20% 70% 50% 60% 30% . .

:

    E () k = 2 :

 

 

 

                                                 0.70 0.60

                        =

                              0.20 0.50 + 0.70 0.60 + 0.10 0.30

 

 

                        = 0.7636


(2)

    450 350 200 1% 2% 3% . .

:

    E k = 3 = 450 + 350 + 200 = 1000

    (4501000) = 0.45

    (3501000) = 0.35

    (2001000) = 0.20  :

 

 

 

                                                 0.35 0.02

                        =

                              0.45 0.01 + 0.35 0.02 + 0.20 0.03

 

                                         10000

   

                                     70

                        =

                              45 + 70 + 60

 

 

                        = 0.4


(3)

            ɡ i40 i60 i6

            i80 i12 . .

            .                ( i0.5) i0.10

:       

            i 1/3

              i  2 / 40

            i  6 / 60 

            i 12 / 80 

            E k = 3 :

 

 

                                                (1/3) (12/80)

                        =

                              (1/3) (2/40) + (1/3) (6/60) + (1/3) (12/80)

               

                                     0.05

                        =

                             0.02 + 0.03 + 0.05

 

                             0.05

                        =

                             0.10

 

                        = 0.05


 

(4)

            ɡ i60 i90 i100

           i70% i60% i50%.

           .        ( i0.34 )  i0.71

            i 250     

            i250/60

            i 250/90

            i 250/100 

            E k = 3 :

 

 

 

                                                (90/250) 0.60

                        =

                           (60/250) 0.70 + (90/250) 0.60 + (100/250) 0.50

               

                                     0.22

                        =

                             0.17 + 0.22 + 0.20

 

                             0.22

                        =

                             0.59

 

                        = 0.37


(5)

i18 :

            i3

            i5

            i6

            i4

    ˿        (i0.25i )

:       

            i18 i3/18 i5/18 i6/18 i4/18

            E k = 4 :

 

 

 

                                                                      (6/18) (3/6)

                        =

                              (3/18) (1/3) + (5/18) (2/5) + (6/18) (3/6) + (4/18) (2/4)

               

                                              0.17

                        =

                             0.06 + 0.12 + 0.17 + 0.12

 

                             0.17

                        =

                             0.47

 

                        = 0.36