Tarea1 PEstoc
November 30, 2022 | Author: Anonymous | Category: N/A
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X 0 , X 1 , . . .
0, 1, 2
0 .1 P = 0.9
0 .7 0
0.2 0.1 0.1 0.8 0.1
p0 = P [X [ X 0 = 0] = 0. 0.3 p1 = P = P [X [ X 0 = 1] = 0. 0.4 p2 = = P P [X [ X 0 = 2] = 0. 0 .3 P [X [ X 0 = 0, X 1 = 1, X 2 = 2]
X 0 , X 1 , . . .
0, 1, 2
0 .7 P P = 0
X 0 , X 1 , . . .
1
N = 5
0.1 0.4 . 0.5
0.3 0.3
2
0, 1, 2
P [X [ X 0 = 1, X 1 = 0, X 2 = 2]
n
P [X [ X 1 = 1, X 2 = 1, X 3 = 0]
X n
α = 0.1
1
3
0.3 0.2 0.5 0.5 0.1 0.4 0.5 0.2 0.3
p0 = 0.5 p1 = 0.5
X 0 , X 1 , . . .
P X 1 = 1, X 2 = 1 X 0 = 0 .
P [X [ X 0 = 1, X 1 = 1, X 2 = 0]
0.5
0.1 X 0 = 1
0, 1, 2
0
2
0 .6 P P = 00..34
0, 1, 2
P =
X 0 , X 1 , . . .
1
3
0.1 0.1 0.8 P P = 0.2 0.2 0.6 . 0.3 0.3 0.4 P X = 1, X = 1X = 0 P X = 1, X = 1X = 0
P X = 1, X = 1X = 0 2
0.1 0.4 .
0.2 0.6 0 .5 0
n = 2
n P 0000 = = P P 1111 = 1 − α
α
0 1
P [X [ X 0 = 0, X 1 = 0, X 2 = 0]
X 0 = 0 {X n } P 1100 = P = P 1100 = α = α 0 < α < 1
0, 1, 2
α
X 0 , X 1 , X 2 , . . .
n
2
α
ξ
{X n }
0, 1, 2
n
.
X 0 = 1
0, 1, 2, 3
P [X [ X 2 = 2]
P 0000 = P 1111 = 1 − α
P [X [ X n = k k]] = 1/4
X n P X 5 = 0 X 0 = 0
.
0.1 0.2 0.4 0.3
0 1
P X n = 0, X 0 = 0
.
0 .2 0 .3 0 .1 0 .4
pi = 1/4 i = 0, 1, 2, 3
X 0 X n P 1100 = P 1100 = α 0 < α < 1
n
X 0 , X 1 , X 2 , . . .
k = 0, 1, 2, 3
0 .3 0 .4 0 .2 0.2 0.1
0.4 0.1 P = 0.3
0 .3 0 .1 0 .3 0 .4 0 .4 0 .1 0 .5
0 .6 P P = 0.3
X n = m´ax ax{ξ 1 , . . . , ξn }
X n n = 0, 1, 2, 3, 4
X n
1 − α
β
0 .5 0 .5 0 0 .5 0 .5 0 .5 0
0 P P = 0.5
X 0 = 0
k = P (ξ ( ξ = k = k)) =
ξ 1 , ξ 2 , . . .
1 − β
P [X [ X 0 = 0, X 1 = 0, X 2 = 0] + P [X [ X 0 = 0, X 1 = 1, X 2 = 0]
X n
” ”
X n = 1
n
X n
0, 1
−
(1 (1,, 1)
1 , X n )
Z n = (X n
X 0 , X 1 , X 2 , . . .
”
0, 1, 2
X n
X 0 = 0
.
(0, (0, 0) (0, (0, 1) (1, (1, 0)
.
0.1 0.2 1
X 0 = 0
.
0.2 0.5 0
0
0 .7 P P = 0.3
1−α 1−β β
α
P P =
0.01 0.12 0.88
0.99
P =
”
T T = = m´ın{n ≥ 0 : X n = 2}
0 1 P X 3 = 0 X 0 = 0, T > 3 2} = { X 3 = 0} ∪ {X 3 = 1}
2
{T > 3}
= {X 3
0 1 2
P (ξ ( ξ n = 0) = 0. 0.4, P (ξ ( ξ n = 1) = 0. 0.3, P (ξ ( ξ n = 2) = 0. 0 .3 ,
n
A
n
( t = 1, 2, . . .) t (t .)
A
X n
X n
P (ξ ( ξ = = 3) = 0. 0 .2
X 0 = 3
N
q
B
N
A
S = = 3 P (ξ ( ξ = = 0) = 0. 0.1 P (ξ ( ξ = = 1) = 0. 0.4 P (ξ ( ξ = = 2) = 0. 0 .3
s = 0 S = 3 X n
{X n }
p
α
1 − p
A
A
b a + b + b ≤ 7
p
(a, b)
a = 4
X 0 , X 1 , . . .
$3
1
k
t
k
ξ n
(N −k)/N
s
n
(s, S )
s
0, 1, 2
0, 1, 2
P (ξ ( ξ n = 0) = 0.1 P (ξ ( ξ n = 4) = 0.1
X 0 , X 1 , . . .
X 0 , X 1 , . . .
{X n }
0, 1, 2
$5
0
1
0.2 0.5 0.1 0.4 0.5 0.2 0.3
q
0 .3 P P = 0.5
0.1 0.8 0.2 0.6 0.3 0.3 0.4
S
0 .1 P P = 0.2
0.2 0.1 0.6 0.4 0.5 0 0.5
0 .7 P P = 0
B
ξ 1 , ξ 2 , . . . P (ξ ( ξ n = 1) = 0.3 P (ξ ( ξ n = 2) = 0.3 P (ξ ( ξ n = 3) = 0.2 X 0 , X 1 , . . . P 4411 P 0044
S =6 = S S 1= ξ 47 = 2 ξ 8 = 2 ξ 1 = 2 ξ 2 = 3 sξ 3= =14 S ξ 4= =40 ξ 5 =X 20 ξ X n n = 1, 2, . . . , 8
X n+1
B
N
p
/
k N
X n
n
t + 1
n
A
B
k =n 1, 2 , . . .X . n = 0X
A
k
b = 4
a
$2
2
X 0 , X 1 , . . .
0, 1, 2, 3
0 .1 0 P = 0
0.2 0.3 0.4 0.3 0.3 0.4 0 0.6 0.4 0 0 0
1
Son s Cla Class ss M iid ddle U pp pper 0 .2 0 .1 0 .6 0 .2 0 .4 0 .5
Lower Lower 0.7 Father s Mi Mid ddle 0.2 C lla ass U pp pper 0.1
X 0 , X 1 , . . .
0, 1, 2, 3, 4, 5
A B
2
0
αi ≥ 0 i = 1, 2, . . . , 6 0
1/3 1/2
0 1/4
0 0
0
6
1
0 1/4 0 1/4 0 0
1/3
0 0 1/4 0 0 0 0 1 1/4 0 0 1 0 0 0 0 0
1/3
0 0 1/4 0 1
0 0 0 0 0 0 / 0 / 0
1 0 0 0 3 1 0 /4 /4 0 0 1/8 7/8 0 1/4 1/4 0 1/8 1/3 0 1/6 1/4 0 0 0 0
0
{0, 1, 2, 3, 4, 5} 1/3 0 2/3 0 0 0 1 3 0 /4 0 /4 0 0 2/3 0 1/3 0 0 0 1 4 0 /5 0 /5 0 0 1/4 1/4 0 1 1 0 /4 /4 1/6 1/6 1/6 1/6 1/6 1/6
P P = P P =
0
5
α1 + · · · + α6 = 1
P P =
0
4
3
α α α α α α 1 0 0 0 0 0 0 1 0 0 0 0 P P = 0 0 00 10 01 00 00 1
3 8 1 4
0
1
P =
1/2
0 0 0 0 0
0 0 0 0 0 0
0 1 0 0 0 1/3
0 1/2 0 0 0 0 1 0 0 0 1 0 0 0 1 1/3 0 1/3
.
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