Prove that var(min(X,c))<= var(X) where c is any constant and X is any random variable.?

👨🏻‍🏫 學術台數學

用戶48782

2016-09-28 3:43 pm

回答 (1)

螞蟻雄兵

2016-09-28 11:53 pm

Sol
Var(X)>=0
(1) X>=c
min(X，c)=c
Var[min(X，c)]=Var(c)=0
Var[min(X，c)]<=VAR(X)
(2) X<c
min(X，c)=x
Var[min(X，c)]=Var(X)
So
Var[min(X，c)]<=VAR(X)

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