قوانين الاحتمالات هام جدا فيه lو dobs
TRANSCRIPT
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-
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3 5 2 2V X
1 2
Ln Ln
Ln
- + - =
+
-
.12
. f a 1
f1
02
11
2
12 :
) ( ) (1 12 2
11 mil mil
t t2 a at t f
> >
= - =
) ( ) (1 1 12 2 2
1mil mil mil
t t t2 a at f t t f
< < <
= = =
f12 .1 0] [ f a 1 0] [ f
) (1
0
) ( ) ( : =td t f11
21
012
= +td t f td t f1
) ( : 1
21
12
= - + a a atd t td1 .
:
12 21
2
12 0
11
2 2t
a a at t = - +
: 1 1
18 2 2 8 a a
= - - - + a a a
-
1: 4 a
== a4:
2
: lack6,0lack1,0
) ( ) (6,0 5,0
5,0 1,0
) ( ) ( ] [ + =td t f t f6,0
1,0
=td t f pX6,01,0
) ( ) ( ] [6,0 5,0
5,0 0
- + =td t tdt pX4 4 4 6,01,02 26,0 5,0
5,0 0 - + = t t t2 4 2
- - - + = 5,0 2 5,0 4 6,0 2 6,0 4 5,0 22 2 2) ( ) ( ) ( ) ( ) (+ - - + =5,0 2 27,0 4,2 5,0=56,0
3
:X E) (
) ( ) (1
21
012
) ( ) ( + =td t f t td t f t. .1
0
=td t f t X E.
) ( ) (1
212 2
012
- + =td t t td t X E4 4 .4
1 1 4 12
6 2 3 6 - - - + =
11
23 2 3
10
2
4 42
3 3 - + = t t t
-
2 1 21 1 1 4 1 ) ( : 2 2 2 3 6
= - + - = - - + = X E
.13
: 1
X
.
. 0410 X
041 0] [ a 1 ) ( : f
0 041 = t f
-
1 ) ( : 041
= t f
: 0 0
1 1041 041
= = td a a
) ( ) ( ] [ a0
td t f pX0 a
= a
0) ( ] [ : X041
p= a a
2
X E) ( :
) ( ) (2 041 041041
0 0 0
1.
082 041t
tdt td t f t X E
= = =
) ( ) ( ) ( : 2 2
041 041 04107
2 2 041 082 = = = =niM X E
-
05 3
pX041 05) ( ] [041041
0505
1 1041 041
) ( ) ( ] [ = = x xd041
05
=td t f pX041 059 09 05 04141 041 041 041
= = - =
041 059 ) ( ] [ : X41
= p
.14
1
pX05 0) ( ] [ : 05
) ( ) ( ] [05 05
10, 0
0 0
td e td t f pX.10 , 0 05 0 = = -
0 10, 0 05 10,0 10, 005
0
+ - = - - - -e e et
; - =4 ,0 6 ,0 1
. 05 2
10, 0 ) ( [ [05
10,0 mil 05x
tx X
-td e p +
= +x mil5, 0 10, 0
x - -e e
+ + - =
10, 0
05mil
tx
x -e
+ - =
= -e5,0=606,0
-
.15
(1
.5 5
: (2
05 5 01
2 ,0 01: 05
= =p
= - = -p8,0 2,0 1 1:
2,0 (3
: (4
Xi10
X pi X) (2,08,0
= = X E2,0 2,0 1 ) ( = =6,1 8,0 2,0 X V) (
; sX62,1 ) ( : = = sX6,1 X V) ( ) ( .16
= =B p A p5,0 ) ( ) ( : .025,0:
:
5 ,0 . 5,0 0202) ( ) ( ) (kk k
C k pX -
k02 ,... ,2 ,1 ,0} { = . 6 1
21:A 02 6
-
: pX21) ( 5,0 !0202) (
!21.!8 =C pX5 ,0 5 ,0 . 2102218 21) ( ) ( ) ( =
; pX900,0 21) ( : 01 -2
:A 01
. ( 02 )
: pX02) ( =C pX5,0 5,0 . 0202020 02) ( ) ( ) ( =5,0 .102) (
; pX359000000,0 02) ( .17
:pk
6,0
4,0
. 01
4,001 px
01 k:
:
6,0 . 4,0 .0101) ( ) (kk k
C pk -
k01,...,2 ,1 ,0} { : = 3 -
:
=C p6,0 . 4,0 .01 337 3) ( ) (
-
; p12,0 3: = p6399720,0 460,0 021 3
.18
1
5 ,4 ,3 ,2 ,1} {
5 4 3 2 1: 15
= = = = =p p p p p
.
2
5 ,4 ,3 ,2 ,1} { .51
:d2 3
) (5
22
1
i
i ii
p f d =
=
- =
: 5 4 3 2 1
12 ,0
5= = = = = =p p p p p
2
01221,0
00011 = = f
02222 ,0
0001= = f
4
09191,0
00013 = = f
00202,0
0001= = f
5
08181,0
0001 = = f
- + - + - = d02,0 02,0 02,0 12,0 02 ,0 22,0 22 2 2) ( ) ( ) ( : - + - +02 ,0 81,0 02 ,0 91,02 2) ( ) (
+ + + + = d20 ,0 10 ,0 0 10 , 0 20 ,02 22 2 2 2) ( ) ( ) ( ) (= d100,0 2:
-
D d9 2: 3
.19
: X
) ( ] [ : b
t
a
= - l ltd e b a p840,00010
= p1 ...840,0 001 0) ( ) ( ] [ : ) ( ] [ :
001
0
= - l ltd e pt 001 00 001 001 ) ( ] [ :
0 + - = - = - - l le e e pt 001 0
l - = -e p2 ... 1 001 0001) ( ) ( ] [ = - - l e840,0 1001: (2) (1)
l = -nl e nl259 ,0 001: = - l e259,0 001:
259,0: = - lnL259 ,0 001: 001
= lnL - ; l94000,0:
: X
= -e t ft 94000,094000,0 ) ( : 081 -2
) ( ] [081
94000, 0
0
= -td e pt 94000,0 081 0- = - = - -e e p1 1 081 02880, 0 081 94000,0 ) ( ] [ ;480,0
. 081 3
-
081
. 081
- = +p p08 1 0 1 081) ( ] [ ) ( [ [ : - =480,0 1
=619,0
: 4
1: 94000 ,0
X E1 ) ( ; l
=
; X E0402 ) ( : .0402