XΩRk
x∈Rk{X≤x} ∈ A
X
F(x) = F(x1, ..., xk) = P r (X≤(x1, ..., xk)).
X= (X1, ..., Xk)
P r(X1≤x1, ..., Xk≤xk) = F(x1, ..., xk).
X= (X1, ..., Xk) (Ω,A, P r)
X1, ..., XkB1, ..., Bn∈B
P r (X1∈B1, ..., Xk∈Bk)=
k
Y
1
P r(Xi∈Bi).
F(x1, ..., xk)
Fi(xi),i= 1, ..., k limxj→∞,∀j6=iF(x1, ..., xk).
X1, ..., Xk
F(x1, ..., xk) =
k
Y
1
Fi(xi).
X1, ..., Xk
ϕ1, ..., ϕkϕ1(X1), ..., ϕk(Xk)
X= (X1, ..., Xk)∈Rk
f(t1, ..., tk), x1, ..., xk∈R
F(x1, ..., xk) = Zxk
−∞ ... Zx1
−∞ f(t1, ..., tk)dt1...dtk.
Z∞
−∞ ... Z∞
−∞ f(t1, ..., tk)dt1...dtk=1.
•XR+
f
EX=Z∞
−∞ xf(x)dx,
X
•X
X X =X+−X−
X+= max{X, 0}X−=−min{X, 0}. X+X−
X
EX=EX+−EX−.
X