. , . , , .
.
2 (, b), 4 :
b b b b
2 . 2 , , () . , = 1/2;
p2 = 1/4.
2 q × q = q2 = 1/4.
.
p × q = 1/2 × 1/2 =1/4, , . . 2 × q = 1/2.
, , .
:
( +q)2 = p2 + 2pq + q2., p = 1/2 (1/2 + 1/2)2 = 1/4+1/2+1/4.
3 , b, , 8 :
ab abc abc abc abc abc abc abc
3 1/8, 2 ( ) 3/8, 2 3/8, 1/8. 3 3.
:
( + q)3 = p3 + 3p2q + 3pq2 + q3.
p = q = 1/2 (1/2 + 1/2)3 = 1/8 + 3/8 + 3/8 + 1/8, . e. , .
n, n, n1, n2 . . :
( + q)n
n, :
N × (p+q)n
, N = 200 n 200×(p+q)2 = 200×(2+2×q+q2). p = q = 1/2, : 50 + 100 + 50.
200 (N = 200) 50 , 100 50 .
N, n = 3 : 25 + 75 + 75 + 25, 3, 2, 1 , N.
200 25 3 (), 75 2 (), 75 2 () 25 3 .
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, , n, n1, n2.... . , q, . .
, , . . .
() . , , .
, , , , :
(3.1)
n ; ; q ; N ().
n = 6 26 = 64 . , . . = q = 0,5, :
64(0,5 + 0,5)6 = 64 [1/64 + 6/64 + 15/64 + 20/64 + 15/64 + 6/64 + 1/64] = 1+6+15 + 20 + 15 + 6+1
m , , ( 3.1). , , .
( p = q = 0,5) ( 3.1). , , .
, , , . , = q = 0,5, . n+1,
n = 1 2 . . 2n, , n = 6; N = 26 = 64.
q , , , n. n, 30 , . , , m .
3. 1
3.1
n | N=2n | |||||||||||
|
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( m n ) :
(3.2)
n m, ;
( );
q = 1 ; m ; n ; n! m! , . .: 1×2×3×...× n 1×2×3×...× m.
m = 1, 2, 3,...n .
, , p = q = 0,5, n = 6
m = 0, 1, 2,..., 6 :
m = 0
m = 1
m = 2
m = 3, 4, 5, 6 :
20/64; 15/64; 6/64; 6/64 . . , .
: μ = np .
m = n = 6 0,5 = 3
s2 = npq = 6 × 0,5 × 0,5 = 1,5.