n . , , .. . , ( ). , , p, .. q = 1 - p. .
: ( - - 0,5); - - ; , , ( ); . .
. , n k
( . 4).
1. , 4 2 ,
p - - 1/6, q = 5/6, n = 4, k = 2.
2. p = 0,6. , 3 ?
n = 5, k = 3, q = 1 - p = 0,4,
.
3. 4 2 . 6 1 , , . , 4 ?
, . p= 4/6 = 2/3 ( 6 4 ), q = 1 - p = 1/3. n= 6, k = 5 k = 6,
.
4. p = 0,6. , ?
2: . (): = { 4 2 } ={ }. P(A)
,
a P(B) = p = 0,6.
, - n- ,
.
5. p = 0,6. , 5 2 ?
, 5(0) + 5(1) + 5(2) + 5(3) + 5(4) + 5(5) = 1. :
, :1- P5(0)-P5(1)=1-0,45-5 0,44 0,6 = 0,91296.
12.
, . , 100
|
|
,
. , 10-15. n , .
( )
, ,
, n. n, k, p, q - , . j(x) : j(-x) = j(x). : , x > 4 j(x) = 0. , j(x), . , , , ( ).
1. 50 100 100(50) . n = 100,k = 50,p=0,5, q = 0,5, k - np = 0,
.
2. 47 57 100 .
( n > 15) : n(k1,k2) n k1 k2
n, p, q , 1: n=100, p = q =0,5, k1=47, k2 = 57.
F (. ).
(x) : (-) = - (). > 5 , () = 0,5.
, 100(47,57) = (1,4) + (0,6). (1,4) = 0,4192, (0,6) = 0,2257, 100(47,57) = 0,6449.
p ( 0,1) n -
, l = np
l , (. . p ).
3. 50 100 . : , 1 , 2 , 3 ?
, 1/50 = 0,02, () n = 100. p , l = np = 2. ,
(.. 0! = 1)
, .
, -2 100(1) 100(2).
: 1 2 , .
3