證明：
Var(X) = E[Var(X|Y)] + Var(E[X|Y])
先求 E[Var(X|Y)]
2 2
= E[E[X |Y]] -E(E[X|Y])
2 2
=E[E[X |Y]]-E[E(X|Y)]
2 2
=E[X ] - E[E(X|Y) ]
接下來看不懂
2 2 2 2 2
=E[X ] - E[X] - E[E(X|Y)] + (E[E[X|Y]]) (E[X] 哪裡來的？)
= Var(X) -Var(E[X|Y])