Теория вероятностей и математическая статистика. Билялов Р.Ф. - 132 стр.

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χ
2
F
χ
2
α,m
χ
2
α,m
P (χ
2
m
> χ
2
α,m
) = α,
χ
2
m
χ
2
m
χ
2
m
p
χ
2
m
(x) =
1
Γ(
n
2
)2
n/2
x
n
2
−1
e
−
x
2
, x > 0.
m \ α 0.9 0.10 0.05 0.02 0.01 0.005
1 0.00016 2.7 3.8 5.4 6.6 7.9
2 0.020 4.6 6.0 7.8 9.2 11.6
3 0.115 6.3 7.8 9.8 11.3 12.8
4 0.30 7.8 9.5 11.7 13.3 14.9
5 0.55 9.2 11.1 13.4 15.1 16.3
6 0.87 10.6 12.6 15.0 16.8 18.6
7 1.24 12.0 14.1 16.6 18.5 20.3
8 1.65 13.4 15.5 18.2 20.1 21.9
9 2.09 14.7 16.9 19.7 21.7 23.6
10 2.56 16.0 18.3 21.2 23.2 25.2
11 3.1 17.3 19.7 22.6 24.7 26.8
12 3.6 18.5 21.0 24.1 26.2 28.3
13 4.1 19.8 22.4 25.5 27.7 29.8
14 4.7 21.1 23.7 26.9 29.1 31.0
15 5.2 22.3 25.0 28.3 30.6 32.5
16 5.8 23.5 26.3 29.6 32.0 34.0
17 6.4 24.8 27.6 31.0 33.4 35.5
18 7.0 26.0 28.9 32.3 34.8 37.0
19 7.6 27.2 30.1 33.7 36.2 38.5
20 8.3 28.4 31.4 35.0 37.6 40.0
21 8.9 29.6 32.7 36.3 38.9 41.5
22 9.5 30.8 33.9 37.7 40.3 42.5
23 10.2 32.0 35.2 39.0 41.6 44.0
24 10.9 33.2 36.4 40.3 43.0 45.5
25 11.5 34.4 37.7 41.6 44.3 47.0
5.4   χ2 -ðàñïðåäåëåíèå è F -ðàñïðåäåëåíèå
Çíà÷åíèÿ ôóíêöèè χ2α,m .
   Ôóíêöèÿ χ2α,m îïðåäåëÿåòñÿ ðàâåíñòâîì P (χ2m > χ2α,m ) = α, ãäå
ñëó÷àéíàÿ âåëè÷èíà χ2m èìååò χ2 -ðàñïðåäåëåíèå ñ m ñòåïåíÿìè ñâî-
áîäû. Ïëîòíîñòü ðàñïðåäåëåíèÿ χ2m ðàâíà
                                 1           n
                                               −1     x
                pχ2m (x) =               x   2      e− 2 , x > 0.
                             Γ( n2 )2n/2
           m\α    0.9          0.10    0.05     0.02      0.01 0.005
             1    0.00016       2.7     3.8      5.4       6.6   7.9
             2    0.020         4.6     6.0      7.8       9.2 11.6
             3    0.115         6.3     7.8      9.8      11.3 12.8
             4    0.30          7.8     9.5     11.7      13.3 14.9
             5    0.55          9.2    11.1     13.4      15.1 16.3
             6    0.87         10.6    12.6     15.0      16.8 18.6
             7    1.24         12.0    14.1     16.6      18.5 20.3
             8    1.65         13.4    15.5     18.2      20.1 21.9
             9    2.09         14.7    16.9     19.7      21.7 23.6
            10    2.56         16.0    18.3     21.2      23.2 25.2
            11    3.1          17.3    19.7     22.6      24.7 26.8
            12    3.6          18.5    21.0     24.1      26.2 28.3
            13    4.1          19.8    22.4     25.5      27.7 29.8
            14    4.7          21.1    23.7     26.9      29.1 31.0
            15    5.2          22.3    25.0     28.3      30.6 32.5
            16    5.8          23.5    26.3     29.6      32.0 34.0
            17    6.4          24.8    27.6     31.0      33.4 35.5
            18    7.0          26.0    28.9     32.3      34.8 37.0
            19    7.6          27.2    30.1     33.7      36.2 38.5
            20    8.3          28.4    31.4     35.0      37.6 40.0
            21    8.9          29.6    32.7     36.3      38.9 41.5
            22    9.5          30.8    33.9     37.7      40.3 42.5
            23    10.2         32.0    35.2     39.0      41.6 44.0
            24    10.9         33.2    36.4     40.3      43.0 45.5
            25    11.5         34.4    37.7     41.6      44.3 47.0


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