概率论随机变量的相互独立和两两独
1.
X,Y独立,则(X(1),...,X(s)),(Y(1),...,Y(n))独立
==>
P(a(1)<X(1)<b(1),...,a(s)<X(s)<b(s),
c(1)<Y(1)<d(1),...,c(n)<Y(n)<d(n))=
=P(a(1)<X(1)<b(1),...,a(s)<X(s)<b(s))*
P(c(1)<Y(1)<d(1),...,c(n)<Y(n)<d(n))
2.
X(1),...,X(s)独立,Y(1),...,Y(n)独立
==》
P(a(1)<X(1)<b(1),...,a(s)<X(s)<b(s))*
P(c(1)<Y(1)<d(1),...,c(n)<Y(n)<d(n))=
=P(a(1)<X(1)<b(1))*...*P(a(s)<X(s)<b(s))*
P(c(1)<Y(1)<d(1))*...*P(c(n)<Y(n)<d(n))
==>
X(1),...,X(s),Y(1),...,Y(n)独立.