. , , [3, 5].
, . . x 1, x 2, , xn. . xi , n. - , (), . . . , , .
x 1 n 1 , x 2 n 2, xk nk , n 1 + n 2 + + nk = n. , , , ni , ω i = ni / n (). , .
. nx , x. X<x nx / n. x : Fn (x) = nx / n. Fn (x) : Fn (x) , [0 1]; x 1 , xk , F (x) = 0, x < x 1, F (xk) = 1, x > xk . F (x) , . Fn (x) F (x) , , X < x. , Fn (x) F (x) n. , F (x) Fn (x). Fn (x) . Fn (x) . x, , Fn (x) , 1/ n, l l / n.
2.1. , . 2.1.
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2.1
i | ||||||
xi |
. , , . 2.2.
2.2
i | ||||||
Xi |
, . 2.1:
( , , n >40) . , . k h , :
. 2.1.
5 7 . ; . k 6 7. , , k 10 20. (n >1000) . k =1,441ln(n)+1; h= (x max x min)/k, x max x min . .
: ; ; i- [xi xi+1] ni ( vi) . .
, . , , h, . . i- n i ni /(nh). fn (x), . .
, , , . : , . , .
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2.2. xi 1000 . , , . 2.3. .
i | |||||||||||
xi | 25,79 | 25,98 | 25,98 | 26,12 | 26,13 | 26,49 | 26,52 | 26,60 | 26,66 | 26,69 | 26,74 |
i | |||||||||||
xi | 26,85 | 26,90 | 26,91 | 26,96 | 27,02 | 27,11 | 27,19 | 27,21 | 27,28 | 27,30 | 27,38 |
i | |||||||||||
xi | 27,40 | 27,49 | 27,64 | 27,66 | 27,71 | 27,78 | 27,89 | 27,89 | 28,01 | 28,10 | 28,11 |
i | |||||||||||
xi | 28,37 | 28,38 | 28,50 | 28,63 | 28,67 | 28,90 | 28,99 | 28,99 | 29,03 | 29,12 | 29,28 |
. , , k = 6.
h= (x max x min)/k = (29,28 25,79)/6 = 0,58.
, . 2.4.
2.4
i | ||||||
xi | 25,79 | 26,37 | 26,95 | 27,53 | 28,12 | 28,70 |
n i | ||||||
n i =ni /n | 0,114 | 0,205 | 0,227 | 0,205 | 0,114 | 0,136 |
z i=n i /h | 0,196 | 0,353 | 0,392 | 0,353 | 0,196 | 0,235 |
, . 2.2, , . 2.3.
, . 2.3, , . 2.1 ( 1/ n, ).