Задания
.pdfP{X = 2} = p2, P{X = 3} = 2p(1 − p), P{X = 4} = (1 − p)2.
x =
2.
EX, DX. X
[0;
θ2 = (n+1)X(n)/n θ
λ2 = n−1
nX
1, . . . , Xn) (X p
p (0; 1) p
k
1, . . . , Xn) (X m,p
p
p m
θ
θ 1 |
t |
[0; 1] |
2 |
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[0; |
θ |
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θt |
t/θ t |
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− |
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2 |
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fθ(t) = { |
3t2θ−3, |
t [0; θ]; |
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0, |
t ̸ [0; θ]. |
θ > 0
−αt
α(t) = αe t > 0 f
2
α
2 α σ
2 α σ
Y = (Y1, . . . , Yn)
Yj = a0 + a1 cos |
2πj |
+ b1 sin |
2πj |
+ εj; |
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n |
n |
Yj = a + bj + cj2 + εj.
1, . . . , Xn) (X p
p (0; 1) p
f(t, p) = pt(1 − p)1−t t
1, . . . , Xn) (X m,p
p
α
α > 0
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{ |
θ |
, t ≥ 1; |
fθ(t) = |
tθ+1 |
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0, t < 1. |
{ |
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fθ(t) = |
e θ − t , t ≥ θ; |
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0 , t < θ. |
θ
2
α
2 α σ
2 α σ
i = xi + θ + εYi i = 1, . . . , n i, θ R x
2
i = θxi + εi Yi = 1, . . . , n i, θ Rx
xi
2
Y > 0
x > 0
i =Y θ/xi + εi
ln=Y ln(θ/x ) + ε
i i i
i = 1, . . . , n θ
i = a + bxi + εi i = 1, . . . , n Y
a, b
2 σ
1 = 1 1Y= 0 2x= 2 2Y= 2, 5 3x= x3
Y3 = 0, 5
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X |
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f(t) = |
1 |
, |
t R. |
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π(1 + (t − θ)2) |
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θ θ R
θ n = 1
λ
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−|t−a|/2 a |
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R |
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a
a
a
a
a
σ
2
a,1
: a = 0 H: a = 1.
0 1
c
H0 X1 ≤ c.
c
ε H : θ = 1
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0 |
H |
1 |
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0 : a = 0H 1 : a =H1 0
(n) X< 3
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F (t) F sup(t) |
= 0, 2 |
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−∞<t<∞ | n |
− 0 | |
1 = 2048 |
2 = |
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4040 |
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n − ν1 = 1992
n = 4000
0 1p= 1/2, p2 = p3 = 1/4 j = Pp(Aj)
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Σ |
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0 H
m2
i
i
α = 0, 05
i
mi Σmi = 576
X Y
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X |
Y |
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( |
X, Y ) |
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X Y |
X
Y
X
Y
X
Y
X
Y
X
Y
X
Y
X
Y
X
Y
X
Y
X
Y
X
Y
X
Y
X
Y
X
Y
X
Y
X, Y 2
(X, Y )
2,2
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n,m |
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X = |
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Y = |
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X, Y |
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sup |
t R |
F |
(t) |
− |
F |
(t) |
= 0, 1 |
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2,m |
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X, Y |
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2 |
= 15 |
2 |
S |
x |
S = 10 |
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y |
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X = 2 Y = 12
, Y ), . . . , (X(X, Y )
1 1 4 4
, Y ), . . . , (X(X , Y )
1 1 100 100
n
1.
2.
3.
4.
5.