6
17
{1, . . . , 6}
&! = x, y, z : x, y, z " {1, . . . , 6}
#&! = 63 = 216.
6
"
"
"
{3, 2, 1}
A
A = x, y, z " &! : x + y + z = 6 ,
#A = 3 + 6 + 1 = 10
10 5
(A) = = H" 0,046.
216 108
17
B
B = x, y, z " &! : x + y + z = 17 ,
#B = 3
3 1
(B) = = H" 0,014.
216 72
A )" B = "
(A )" B) = 0 = (A) (B),
A B
(A) 0,019 0,023 0,028 0,032 0,036 0,037 0,039 0,042 0,046 0,051
0,054 0,056 0,060 0,083 0,130 0,167 0,194
(B) 0,009 0,012 0,014 0,018 0,019 0,028 0,083 0,792
2
&! = (0; 20) \ {10},
|&!| = 20.
x " &!
" x 10 - x x < 10
" x - 10 20 - x x > 10
f(x)
Å„Å‚
ôÅ‚
ôÅ‚
x(10 - x), x < 10
òÅ‚
f(x) =
ôÅ‚
ôÅ‚
ół
(x - 10)(20 - x), x > 10
A
A = x " &! : f(x) 21 .
- x2 + 10x - 21 0 - x2 + 30x - 221 0
" = 16 " = 16
x1 = 3, x2 = 7 x1 = 13, x2 = 17
x " (- ", 3] *" [7, ") x " (- ", 13] *" [17, ")
A = (0, 3] *" [7, 10) *" (10, 13] *" [17, 20),
|A| = 12
12
(A) = = 0,6.
20
x " &! g(x)
Å„Å‚ Å„Å‚
ôÅ‚ ôÅ‚
ôÅ‚ ôÅ‚
|x - (10 - x)|, x < 10 |2x - 10|, x < 10
òÅ‚ òÅ‚
g(x) = =
ôÅ‚ ôÅ‚
ôÅ‚ ôÅ‚
ół ół
|(x - 10)(20 - x)|, x > 10 |2x - 30|, x > 10
B
B = x " &! : g(x) < 2 .
|2x - 10| < 2 |2x - 30| < 2
- 2 < 2x - 10 < 2 - 2 < 2x - 30 < 2
8 < 2x < 12 28 < 2x < 32
x " (4, 6) x " (14, 16)
B = (4, 6) *" (14, 16),
|B| = 4
4
(B) = = 0,2.
20
A )" B = "
(A )" B) = 0 = (A) (B),
A B
(A) 0 0,2 0,21 0,3 0,4 0,6 0,7 0,755 1,31
(B) 0,1 0,19 0,2 0,36 0,4 0,5 0,56 0,6
2
&! = (0; 20) \ {10},
|&!| = 20.
x " &!
" x 10 - x x < 10
" x - 10 20 - x x > 10
f(x)
Å„Å‚
ôÅ‚
òÅ‚
x(10 - x), x < 10
f(x) =
ôÅ‚
ół
(x - 10)(20 - x), x > 10
A
A = x " &! : f(x) 21 .
- x2 + 10x - 21 0 -x2 + 30x - 221 0
" = 16 " = 16
x1 = 3, x2 = 7 x1 = 13, x2 = 17
x " (- ", 3] *" [7, ") x " (- ", 13] *" [17, ")
A = (0, 3] *" [7, 10) *" (10, 13] *" [17, 20),
|A| = 12
12
(A) = = 0,6.
20
x " &! g(x)
Å„Å‚ Å„Å‚
ôÅ‚ ôÅ‚
ôÅ‚ ôÅ‚
|x - (10 - x)|, x < 10 |2x - 10|, x < 10
òÅ‚ òÅ‚
g(x) = =
ôÅ‚ ôÅ‚
ôÅ‚ ôÅ‚
ół ół
|(x - 10)(20 - x)|, x > 10 |2x - 30|, x > 10
B
B = x " &! : g(x) < 2 .
|2x - 10| > 2 |2x - 30| > 2
2x - 10 < -2 2x - 10 > 2 2x - 30 < -2 2x - 30 > 2
2x < 8 2x > 12 2x < 28 2x > 32
x < 4 x > 6 x < 14 x > 16
x " (- ", 4) *" (6, ") x " (- ", 14) *" (16, ")
B = (0, 4) *" (6, 10) *" (10, 14) *" (16, 20),
|B| = 16
16
(B) = = 0,8.
20
A ‚" B
(A )" B) = (A) = (A) (B),
A B
(A) 0,16 0,21 0,3 0,6 0,84 10,67
(B) 0,2 0,4 0,6 0,8 0,96
10
2
3
p
&! = x, y : x, y " {1, . . . , 6} ,
#&! = 62 = 36.
A = x, y " &! : x = y = x, x : x " {1, . . . , 6} .
#A = 6
6 1
p = = .
36 6
2
1
(S10 2) = 1 - (S10 < 2) = 1 - (S10 = k) =
k=0
1
k 10-k
10
= 1 - 1/6 5/6 H" 1 - (0,1615 + 0,3230) = 0,5155.
k
k=0
3
3
(S10 3) = (S10 = k) =
k=0
3
k 10-k
10
= 1/6 5/6 H" 0,1615 + 0,3230 + 0,2907 + 0,1550 = 0,9302.
k
k=0
([S10 2] )" [S10 3]) = (2 S10 3) =
3
k 10-k
10
= 1/6 5/6 H" 0,2907 + 0,1550 = 0,4457 = 0,4794 H" (S10 2) (S10 3),
k
k=2
[S10 2] [S10 3]
(S10 2) -3813,6973 7,88 · 10-13 10-10 0,022 0,0299 0,03 0,0321 0,0702 0,1032 0,15 0,2083
0,2639 0,4167 0,4963 Ä… 0,2778 0,5155 0,9133 0,5646 0,5738 Ä… 0,0309 0,8385 0,9478
1 - 1,58 · 10-13
(S10 3) -0,55 2,89·10-13 0,0003 0,0024 0,4417 0,5593 0,7209 0,9117Ä…0,2778 0,9303
0,9872 0,9909 Ä… 0,0309 0,9985 0,9998 0,9999 1,4167 5950,9277
a = 10 d = 5
d < a
10
|&!| = 102 = 100.
A A &!
|A| = Ä„ · (10/2)2 = 25Ä„
25Ä„ Ä„
(A) = = H" 0,785.
100 4
B B 5
A
25
|B| = |&!| - Ä„ · (5/2)2 = 100 - Ä„
4
25
100 - Ä„ Ä„
4
(B) = = 1 - H" 0,804.
100 16
(A | B) A )" B
75
|A )" B| = |A| - Ä„ · (5/2)2 = Ä„
4
75
Ä„ 3
4
(A )" B) = = Ä„.
100 16
3
(A )" B) Ä„ 3Ä„
16
(A | B) = = = H" 0,733.
Ä„
(B) 1 - 16 - Ä„
16
(A | B) = (A),
A B
(A) 0,589 0,785
(B) -0,186 0,196 0,568 0,607 0,804 0,866 2,945 0,951 73,297
(A | B) -3,161 -0,023 0,188 0,2 0,473 0,63 0,589 0,650 0,652 0,733 0,75
0,970 0,977 73,297
[1, 5]
[3, 6]
5
5
H1 5
H2 5
A 5
H1 )" H2 = " H1 *" H2 = &!
2 1
(H1) = = , 2 6
6 3
2
(H2) = 1 - (H1) = ,
3
1
(A | H1) = , 1 5
5
1
(A | H2) = , 1 4
4
1 1 2 1 1 1 7
(A) = (H1) (A | H1) + (H2) (A | H2) = · + · = + = H" 0,233.
3 5 3 4 15 6 30
1 1
(H1) (A | H1) · 2
3 5
(H1 | A) = = = H" 0,286.
7
(A) 7
30
(A) 0,0008 0,15 0,208 0,217 0,233 0,327 0,367 0,567
(H1 | A) 0,006 0,033 0,059 0,067 0,095 0,1 0,104 0,11 0,122 0,128
0,143 0,286 0,385 0,45 0,75 0,8
K
M
D
K )" M = " K *" M = &!
1
(K) = (M) = ,
2
25
(D | K) = ,
1000
5
(D | M) = .
100
1 25 1 5 75 3
(D) = (K) (D | K) + (M) (D | M) = · + · = = = 0,375.
2 1000 2 100 2000 80
1 5
(M) (D | M) · 50 2
2 100
(M | D) = = = = H" 0,67.
75
(D) 75 3
2000
(D) 0,375 0,4875
(M | D) 0,05 0,67 1,33
n = 20
m = 3
p = 4
p
&! = x, y : x, y " {O, R} ,
#&! = 22 = 4.
A = x, y " &! : x = y = x, x : x " {O, R} .
#A = 2
2 1
p = = .
4 2
3
2
(S20 3) = 1 - (S20 < 3) = 1 - (S20 = k) =
k=0
2
k 20-k
20
= 1 - 1/2 1/2 H" 1 - (0,000001 + 0,00002 + 0,00018) H" 0,99980.
k
k=0
4
4
(S20 4) = (S20 = k) =
k=0
4
k 20-k
20
= 1/2 1/2 H" 0,000001 + 0,00002 + 0,00018 + 0,00109 + 0,00462 H" 0,00591.
k
k=0
([S20 3] )" [S20 4]) = (3 S20 4) =
4
k 20-k
20
= 1/2 1/2 H" 0,00109 + 0,00462 = 0,00571 = 0,00591 H" (S20 3) (S20 4),
k
k=3
[S20 3] [S20 4]
(S20 3) 0,001 0,00211 0,238 0,24 0,99980 0,99981
(S20 4) 0,00129 0,00591 0,00845 0,009 0,05909 0,2 0,8
r = 10
d = 5 d < r
10
|&!| = Ä„ · 102 = 100Ä„.
A A &!
"
|A| = (10 2)2 = 200
200 2
(A) = = H" 0,64.
100Ä„ Ä„
B B 5
A
|B| = |&!| - 52 = 100Ä„ - 25
100Ä„ - 25 1
(B) = = 1 - H" 0,92.
100Ä„ 4Ä„
(A | B) A )" B
|A )" B| = |A| - 52 = 175
175 7
(A )" B) = = .
100Ä„ 4Ä„
7
(A )" B) 7
4Ä„
(A | B) = = = H" 0,605.
1
(B) 1 - 4Ä„ - 1
4Ä„
(A | B) = (A),
A B
(A) 0,16 0,64 1,57
(B) 0,557 0,79 0,92
(A | B) 0,086 0,09 0,14 0,605 0,988
[3; 6]
[1; 5]
5
5
H1 2
H2 2
A 5
H1 )" H2 = " H1 *" H2 = &!
2 1
(H1) = = , 2 6
6 3
2
(H2) = 1 - (H1) = ,
3
1
(A | H1) = , 1 4
4
1
(A | H2) = , 1 5
5
1 1 2 1 1 2 13
(A) = (H1) (A | H1) + (H2) (A | H2) = · + · = + = H" 0,217.
3 4 3 5 12 15 60
1 1
(H1) (A | H1) · 5
3 4
(H1 | A) = = = H" 0,385.
13
(A) 13
60
(A) 0,15 0,208 0,217
(H1 | A) 0,128 0,333 0,385 0,56
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