12.

, , . , , , , 10 . 0 1 . ..., ~ 0.469 /. 1 . , . , 70- XX .

. . . , ...; [0,1], . . . , . . . , , . . , , -, . . 1, , , . . . ( ). , .

, . . . . . . , . ( - ). , , , . . .

, , . , , .

. . . . X 0 1 2/3 1/3 . 0 [0, 2/3], 1 [2/3,1]. . . . X,

!() = 3, = /3 = log2 3 - 2/3 0.9183 /.,

1[ 3, 1]

0[0, 2] [ I, 1]

10[I, I]

01[ 1,2 ]

00[0, 4]

, 1]

110[I, ] 101[22, I ]

100[ 22,22 ]

011[,3 ] 010[4, ]

001[ 22, | ]

000[0, ^]

31

32 15

16

2

8 3 4 5 8

1

2 3 8

1

4

= 0.11111

= 0. 1111 = 0. 111 = 0. 11 = 0. 101 = 0. 1 = 0. 011 = 0. 01

1

/27 /

27 /

27

2/ 2/

4

2

/22

/22 22 22 22

4/ 4/ 8/

0000

0001

010

001

011

100

101

11.

1 (X) = 65/81 ~ 0.8025 /. (),

1 (X) = 76/81 ~ 0.9383 /. ( ),

1 (X) = ) = 1 /. ().

, . , , - , .

.

1. . . . , , . , . 2. , . . 1. , , 111. 7/8 £ [2/3,1], , 1. 7/8 2/3 1/3, 5/8 £ [0,2/3], , 0. , (5/8 0) * 3/2 = 15/16 £ [2/3,1], 1, . . 101 . , - , , " " 1 . .

► 20

. . ., , -, . , . . . - 0 1.

 

1

2

3

4

2

1 2 5 6 7

V

1/3

1/3

1/6

1/6,

V

0.2 0.1 0.3 0.25 0.15,

1 4

9

16

25

36

49

 

V

0.1 0.1

0.1

0.3

0.1

0.1

0.2,

 

4

-2 -10 1 2

 

V

1/3 1/4 1/5 1/6 1/20.

 

► 21

, . . . ( = ) = 1/3, ( = ) = 2/3.

► 22

011 . . . . , .

23

BAABC, . . . X P(X = A) = 1/4, P(X = B) = 1/2, P(X = C) = 1/4. , X P(X = A) = 1/3, P(X = B) = 7/15, P(X = C) = 1/5?

► 24

. . . X . 4 X . . . X X. X? ..., X ?

► 25

, ( 2 3) ABAAAB, . . . ., , .