2 TD - DLST

N{1,2, . . . , n}X= (1+cos πN)/2
X B(2n, p)Z=|X−n|
n A B
Ω
k A B
K A B
n1n3 1
i= 1,2,3Bi=
N= 11B1+ 11B2+ 11B3N
A B P (A) = 1/2P(B) = 1/3P(A∪B) = 7/12
P(A∩B)P(Ac∩B)P(A∪Bc)P(Ac∩Bc)X= 11A−11B
X
X
X X+= max(X, 0) X−= max(−X, 0)
X|X|X+X−
|IE(X)| ≤ IE(|X|)
X{−1,0,1}α= IE(X)β= IE(|X|)
|α| ≤ β≤1
X α β
n2n
X
(Ω, P )X
XIE(X) Var (X)
Y
(Ω0, P 0)Y
YIE(Y) Var (Y)
n→ ∞
X GX
Var (X) = G00
X(1) + G0 X(1) −[G0 X(1)]2.
X[[0, n]] GX
IE(X) Var (X)
X B(n, p)n∈N0<p<1
GXX Y X B(n, p)Y
B(m, p)n, m ∈N0<p<1X+Y B(n+m, p)

1n n ≥2
X Y S =X+Y
(Ω, P )X Y
X Y E(X)E(Y)E(S)
X Y
n=6 S=X+Y E(S)
Z= max(X, Y )Z GZ(t)E(Z)
n n k
pk
k
4
A=B=
A B A
B
Mi, i = 1,...,4
Mi
n
p
(Ω, P )
Pnne
Pnn→+∞
Ai=
Bi=
4N > 4
N
X
H1
H2
H3
X E(X).