作者chspfang (小汪)
看板Grad-ProbAsk
標題[問題] 台科大工管統計
時間Wed Mar 18 22:25:33 2009
Prove that the inequality
P(X≧1,Y≧1)≦min( E(X) , E(Y) )
holds for any two non-negative continuous random variables X and Y with
joint density f(x,y),where X is not necessarily independent of Y and min(a,b)
equals the smaller value between a and b.
答案
由馬可夫不等式知 P(X≧1)≦E(X) 且 P(Y≧1)≦E(Y)
P(X≧1,Y≧1)≦P(X≧1,Y≧1)+P(X≧1,Y< 1)=P(X≧1)≦E(X)
P(X≧1,Y≧1)≦P(X≧1,Y≧1)+P(X <1,Y≧1)=P(Y≧1)≦E(Y)
=> P(X≧1,Y≧1)≦min( E(X),E(Y) )
答案大概是這樣
可是解答我看不太懂
有強者能出來解釋一下嗎
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1F：推 ericchen:可以由2乘2表來看 03/18 22:31