Добавил:
Upload Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз: Предмет: Файл:

09-01-2015_09-46-11 / Лекция 2 ТВ и МС (1)

.pdf
Скачиваний:
20
Добавлен:
24.03.2015
Размер:
200.77 Кб
Скачать

!"#$%& 2

'!())*+,)'-, -./,0,!,1*, 2,/-341-)4*

!"#$% #&"'()*+) ,-#./012/*$ 12//$ -3*/'*3/ '1#&3 N 0(4*3435236*+7 */#342/#$*+7 1#73834. 9"8/2 *(5+4($% 0(4*3435236*+21 1#738+ , 12/:;1/ 381*(-34+/ <(*#+.

!"#$$%&'$()' )*+','"'-%' .'+)/0-)$0%. !"#$%&'$(&)* #3=+$1> ? *(5+4(/$#> 3$*3</*1/ '1#&( =&(@3.01>$*+7 8&> #3=+$1> ? 1#73834 m(+) - 3=;/2" '1#&" 1#73834

N

 

 

 

 

 

(1.1)

 

 

A(?)=

 

 

 

 

 

B(2/$12, '$3

C302"&(

(1.1) -&(##1'/#-3) 4/03>$*3#$1 .3736( *( 4+0(6/*1/ 8&>

#$($1#$1'/#-3) 4/03>$*3#$1 . D8*(-3 3*1 3$&1'(:$#> .3 #";/#$4" . E$($1#$1'/#-(>

4/03>$*3#$%

4+'1#&>/$#>

$3&%-3 .3 0/5"&%$($(2 ,-#./012/*$(, ( -&(##1'/#-(>

4/03>$*3#$% 236*3 *()$1 83 3.+$(, a priori

,-$.(&-/ 01/((23"(0$. -"#$%&'$(&2

1) F&> &:=3@3 #&"'()*3@3 #3=+$1> ?

0! A(?)! 1

2)!"#$% #3=+$1> ? 1 G */#342/#$*+ ( ?G = ) . H3@8(

A(?+G)= A(?) +A(G)

3) !"#$% ?1 , …,?k – 3=0(5":$ .3&*": @0".." #3=+$1), $3@8( A(?1 )+A(?2 )+…+A(?k ) =1

56"7"89: #;7<%8=9;>%#%

!01 .38#'/$/ '1#&( 1#73834 '(#$3 1#.3&%5":$#> */-3$30+/ .0(41&( 1 C302"&+ -32=1*($301-1, -3$30+/ 1 .014/8/2 *16/.

.>=?%6; @>;%A?"B"8%&

!0>2+2 .03154/8/*1/2 ( 8/-(0$34+2 .03154/8/*1/2) 2*36/#$4

#1 , #2 ,…,#k *(5+4(/$#> 2*36/#$43 4#/7 .3#&/834($/&%*3#$/) 418( :

#1 #2 …#k= {(/1 , /2, …, /k ) | /1 %#1 , /2 % #2,…, ak % #k }

4#/-21$ 5#$26-"7"'2% . I1#&3 ,&/2/*$34 .0>23@3 .03154/8/*1> 2*36/#$4 #1 , #2 , …,#k 0(4*3 .03154/8/*1: '1#&( ,&/2/*$34 #3#$(4&>:;17 /@3 2*36/#$4 :

N(#1 #2 …#k )=N(#1 )N(#2 )…N(#k )

!0(41&3 .03154/8/*1> /;/ *(5+4(:$ 3#*34*+2 5(-3*32 -32=1*($301-1

1%$") +#23'4'-%5 %2 n *) m

C=B=D= ; >=EE=F%?=8%% : ,0$1)0282 (5$($9/82 8$:'$ #/((/72&) 6/ (&$1$8 m 3"1$-"0 26 ;#<55= - n 3"1$-"0 (m ! n) ?

J( ./04+) #$"& 236*3 .3#(81$% 38*3@3 15 n '/&34/-, *( 4$303) - 38*3@3 15 (n-1) '/&34/- , …, *( m-) #$"& – 38*3@3 15 n – (m - 1) = ( n m + 1) '/&34/-. D=;// '1#&3 *(73812 .3 .0(41&" .03154/8/*1> :

1

n(n-1)(n-2)…(n-(m-1))=n(n-1)(n-2)…(n-m+1)=

H(-1/ -32=1*(K11 *(5+4(:$ #/68">"'2%82, 1 3=35*('(:$

=

L#&1 m=n , $3 5(8('( 3 0(##(614(*11 .0/40(;(/$#> 4 5(8('" 3 -3&1'/#$4/

./0/#$(*343- n – ,&/2/*$*3@3 2*36/#$4(.

= n!

1%$") $)&'0#-%5 %2 n *) m

C=B=D= ; ?:<;>" : ,0$1)0282 (5$($9/82 8$:'$ -=9#/&) m 3"1$-"0 26 ;#<55= - n 3"1$-"0 (m ! n) ?

G ,$3) 5(8('/ .30>83- 3$=10(/2+7 m 4 '/&34/- 15 @0"..+ 4 n '/&34/- */ 1@0(/$ 03&1,

$./ 2+ 12//2 8/&3 # */".30>83'/**+2 4+=3032.

G ./043) 5(8('/ -(6832" 4(01(*$"

4+=30(

m '/&34/- #33$4/$#$4"/$ m! 4(01(*$34 0(##(614(*1> ( -3&1'/#$43 ./0/#$(*343-

15 m ).

E&/834($/&%*3 #.3#3=34 0(##(614(*1> 4

m! 0(5 =3&%</, '/2 #.3#3=34 4+=30(.

M3&1'/#$43 #.3#3=34 4+=30( *(5+4(/$#> 32(1$8 ($3"&/'2. 15 n .3 m 1 3=35*('(/$#> :

= =

M&(##1'/#-(> #7/2( >4&>/$#> 2($/2($1'/#-3) 238/&%: #&"'()*+7 ,-#./012/*$34, 4 -3$30+7 1#738+ 3=&(8(:$ 3.0/8/&/**3) #122/$01/) .3 3$*3</*1: - "#&341>2 ,-#./012/*$(, $(- -(- */$ 3#*34(*1) #'1$($% -(-3)-&1=3 15 1#73834 =3&// 4/03>$*+2, '/2 80"@3). H(-12 #43)#$432 , *(.012/0, 3=&(8(:$ 3.+$+ .3 154&/'/*1: *("8('" 3.0/8/&/**3@3 '1#&( <(034 15 "0*+.

-E8;?8:" EG"7: ?:<;>= m H=>;? %A I>8:, E;B">F=J"K n H=>;? % E;;9?"9E9?ILJ%" %7 A=B=D%

I.)G"7= <"A ?;A?>=J"8%&

1),?"8/ 9"6 <5$#%7$3"'2% !"#$% 4 "0*/ n <(034 1 ,-#./012/*$ #3#$31$ 4 $32, '$3 *("@(8 4+*12(:$ m <(034, */ 43540(;(> 17 3=0($*3 , .30>83154&/'/*1> <(034 .01

,$32 */ 4(6/*. H3@8( 3=;// '1#&3 1#73834 ,$3@3 #&"'()*3@3 ,-#./012/*$( 0(4*3 '1#&" #.3#3=34 4+=0($% m <(034 15 n, $./. '1#&" #3'/$(*1) :

N=

2)

,?"8/ ( <5$#%7$3"'2"8

N5 "0*+

# n <(0(21 *("@(8 4+*12(:$#>

 

.3#&/834($/&%*3 m <(034,

*/ 43540(;(> 17 3=0($*3, .30>83154&/'/*1> <(034 .01

 

,$32 4(6/*. H3@8( 3=;// '1#&3 1#73834 ,$3@3

#&"'()*3@3 ,-#./012/*$( 0(4*3 '1#&"

 

0(52/;/*1) 15 n .3 m :

 

 

 

 

N=

 

2

II.)G"7= E ?;A?>=J"8%"7

1),?"8/ 9"6 <5$#%7$3"'2% N5 "0*+ # n <(0(21 m 0(5 4+=10(:$ *("@(8 .3 38*32" <(0" 1 43540(;(:$ <(0 3=0($*3. A/5"&%$($32 3.+$( >4&>:$#> 4#/435236*+/ *(=30+

15 m <(034, 3$&1'(:;1/#> #3#$(432. J(=30+ 15 38*17 1 $/7 6/ <(034,

*3

0(#.3&36/**+7

4 0(5&1'*32 .30>8-/ , #'1$(:$#>

381*(-34+21 (#7/2( =/5

".30>83'/*1>).

!01 ,$32 3$8/&%*+/ *(=30+ 23@"$

#38/06($% .34$30>:;1/#>

,&/2/*$+. H(-12 3=0(532 5(8('( #4381$#> - 4+'1#&/*1: -3&1'/#$4( #.3#3=34 4+=0($%

m ,&/2/*$34 15 n+m-1 ,&/2/*$34 =/5 ".30>83'/*1> .

!3&"'(:;1/#> 4 0/5"&%$($/

8(**3@3 3.+$( -32=1*(K11 *(5+4(:$#> #3'/$(*1>21 # .34$30/*1>21 15 n .3 m,

( 17

3=;// '1#&3 3.0/8/&>/$#> .3 C302"&/ :

 

 

 

N=

 

 

 

 

2),?"8/ ( <5$#%7$3"'2"8 N5 "0*+ 4+=10(:$ m <(034 15 n, 43540(;(> <(0+ 3=0($*3. !01'/2 .30>83- 4+*12(*1> <(034 4(6/*. H3@8( *( ./0432 2/#$/ 236/$ =+$% &:=3) 15 n <(034, *( 4$3032 – $36/ &:=3) 15 n <(034 1 $(- m 0(5. G ,$32 #&"'(/ 0(5&1'*+21

1#738(21 ,-#./012/*$( ="8"$ 4#/435236*+/ m -,&/2/*$*+/ *(=30+ ( 433=;/ @3430>

# .34$30/*1>21), 3$&1'(:;1/#> &1=3 #3#$(432 ,&/2/*$34, &1=3 .30>8-32

17

#&/834(*1>. !3&"'(:;1/#> -32=1*(K11 *(5+4(:$#> 0(52/;/*1>21 # .34$30/*1>21 15 n .3 m, ( 17 3=;// '1#&3 3.0/8/&>/$#> .3 C302"&/ :

N=n&n…n = nm

M";7"9>%D"E#=& ?">;&98;E9N

D=3=;/*1/ -&(##1'/#-3@3 3.0/8/&/*1> 4/03>$*3#$1 *( #&"'() -3@8( #&"'()*+) ,-#./012/*$ 12//$ =/#-3*/'*3/ '1#&3 1#73834, $./. 1#738+ 0(4*3435236*+/, *3 17 "6/ =/#-3*/'*3/ '1#&3

G/03>$*3#$%: #&"'()*3@3 #3=+$1> ? *(5+4(/$#> 3$*3</*1/ 2/0+ 3=&(#$1 (A) , =&(@3.01>$#$4":;/) 8(**32" #3=+$1: - 2/0/ (#), #33$4/$#$4":;/) 4#/435236*+2 1#738(2 ,-#./012/*$( :

P(A) =

@8/ -2/0( ( 8&1*(, .&3;(8%, 3=O/2) ? 1 # #33$4/$#$4/**3.

D'/418*3, '$3 @/32/$01'/#-(> 4/03>$*3#$% "834&/$430>/$ #43)#$4(2 #$($1#$1'/#-3) 4/03>$*3#$1

A(##23$0/**3/ 4+</ -&(##1'/#-3/ 3.0/8/&/*1/ 4/03>$*3#$1 1 /@3 3=3=;/*1/ 4 418/ @/32/$01'/#-3) 4/03>$*3#$1 *(0>8" # 3'/418*+21 83#$31*#$4(21, .0/68/ 4#/@3

.03#$3$3) 1 1*$"1$14*3) *(@&>8*3#$%: , 12//$ 1 0>8 #";/#$4/**+7 */83#$($-34 :

.0/8"#2($014(/$ $3&%-3 -3*/'*3/ 1&1 #'/$*3/ 2*36/#$43 1#73834 #&"'()*3@3 ,-#./012/*$( 1 3=>5($/&%*3 5*(*1> 17 4/03>$*3#$/). G#/ ,$3 8(&/-3 */ 4#/@8( 12//$ 2/#$3, 1 .3,$32" 44/8/**3/ 3.0/8/&/*1/ */ >4&>/$#> 83#$($3'*3 3=;12. G *(#$3>;// 40/2> #$(&3 3=;/.01*>$+2 (-#132($1'/#-3/ .3#$03/*1/ $/3011 4/03>$*3#$/).

3

Соседние файлы в папке 09-01-2015_09-46-11