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Ω = D×D= , , ..., 
D= ,,,,,
Ω6×6 = 36
Ω1
36
⇐⇒
D1
6
(Ω, P r)
ΩP r
Ω [0,1]
X
ω∈Ω
P r(ω) = 1.
•Ω
•A⊂Ω
•P r Ω
•P r P(Ω)
P r(A) = X
ω∈A
P r(ω),∀A⊂Ω
P r(A)A
•P r(∅) = 0
•P r(¯ A) = 1 −P r(A)
•P r(∪i∈IAi) = Pi∈IP r(Ai)
Ai, i ∈IP(Ω)
P r2( ) = P r2( ) = 1
4
P r2( ) = P r2( ) = P r2( ) = P r2( ) = 1
8
Ω = D×D
P r22(dd′) = P r2(d)P r2(d′)
P r22( ) = 1
4.1 8=1 32.
P r22
Ω

A= ,,,,,
P r(A) = X
ω∈A
P r(ω)
1
36 +1 36 +1 36 +1 36 +1 36 +1 36 =1 6.
P r22
1
16 +1 64 +1 64 +1 64 +1 64 +1 16 =3 16.
(Ω, P r) Ω′
XΩ′Ω Ω′
Ω′N R
Ω′P rX
ω′∈Ω′
P rX(ω′) = P r(X−1({ω′}))
P rXΩ′
X
ω′∈Ω′
P rX(ω′) = 1.
A′⊂Ω′
P rX(A′) = P r(X−1(A′))
P rXP r
S(ω)
S(,) = 3 + 6 = 9
S
s
P r11(S=s)1
36 2 36 3 36 4 36 5 36 6 36 5 36 4 36 3 36 2 36 1 36
P r22(S=s)4
64 4 64 5 64 6 64 7 64 12 64 7 64 6 64 5 64 4 64 4 64

R
n
n
EX=X
x∈X(Ω)
x.P r(X=x)
X(Ω)
X X
S
P r11 P r22
•E11S= 2.1
36 + 3.2 36 +... + 12.1 36 =7
•E22S= 2.4
64 + 3.4 64 + 4.5 64 +... + 12.4 64 =7
X
•E1X=1
6.(1 + 2 + ... + 6) = 3.5
•E2X=1
4.(1 + 6) + 1 8.(2 + 3 + 4 + 5) = 3.5
X1X2
(Ω, P r)
α∈R
E(αX1) = αEX1
E(X1+X2) = EX1+EX2
X Y (Ω, P r)
P rXY (X=x, Y =y) = P r({ω∈Ω|X(ω) = x, Y (ω) = y})
x y
X Y x y
P rXY (X=x, Y =y) = P rX(X=x)P rY(Y=y)
X Y
XY
E(XY ) = EXEY

X Y
P r11
P r22 S=X+Y P =XY
•ES=7
2+7 2= 7,EP=7 2.7 2=49 4.
P
•S P
E(S+P) = ES+EP= 7 + 49
4
SP E(SP ) = 637
6
112
ES.EP= 7.49
4=343 4.
X
(Ω, P r)
VX=E((X−EX)2)
1
100
2
0
100 0.98 0.02
0 100
200 0.9801 0.0198
0.0001
1012 2
0.98(0 −2)2+ 0.02(100 −2)2=196.
0.9801(0 −2)2+ 0.0198(100 −2)2+ 0.0001(200 −2)2=198.
σ
σX =√VX.
VX=E(X2)−(EX)2.
X Y
X+Y