Kurs_vysshei_matematiki_UP_Berkov_N.A._2007-2
.pdfξ m n
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xi
n1, n2, . . . , nk
F*(x) |
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0.9 |
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0 F (x) 1 |
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F (x) |
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F (x) = 0 |
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x x1 F (x) = 1 |
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(aj−1; aj ] |
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P = |
(m1 + . . . + ms = n) |
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n · (aj − aj−1) |
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x |
Pi*
0.3
0.2
0.1
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x |
n
1 n
x¯ = n i=1 xi.
1 k
x¯ = n i=1 ni · xi.
S2 = n1 n (xi − x¯)2 = (x − x¯)2
i=1
S2 = n1 k ni(xi − x¯)2
i=1
√
S = S2
S2 = n1 n x2i − (¯x)2 = x2 − x2
i=1
20
h
10
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t
hT =
T T =
tT =
F (x) x
j := 2..M |
F1 := h1 |
Fj := Fj−1 + hj |
F T =
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F |
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0.5 |
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T |
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M x := mean(x) |
M x |
= 150.115 |
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s2 := |
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n |
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· var(x) |
s2 |
= 232.727 |
n− |
1 |
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√ |
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S := s2 S = 15.255
median(x) = 149.515
8an a
ξ
8an = 8a(x1, . . . , xn).
n
ξ1, . . . , ξn
ξ x1, . . . , xn
x1 ξ1 x2 ξ2 8an
8an
8an n → ∞ a
lim P {|8an − a| < ε} = 1 ε > 0.
n→∞
8an a
M (8an) = a.
M (8an) − a n → ∞
8an
x¯
S 2
σ2
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S 2 |
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− |
k |
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S 2 = |
1 |
mi(xi − x¯)2. |
n 1 |
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=1 |
S S
a (a1; a2) a1 = a1(x1, . . . , xn)
a2 = a2(x1, . . . , xn) |
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γ P {a (a1; a2)} = γ |
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γ |
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− |
2 |
√n |
2 |
√n |
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x¯ |
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τ γ |
σ |
; x¯ + τ γ |
σ |
, |
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τ γ
2
Φ(τ γ ) = γ
2 2
x¯