※ 引述《chspfang (小汪)》之銘言： : 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 P(X≧1,Y≧1)+P(X≧1,Y< 1)=P(X≧1) P(X≧1,Y≧1)+P(X <1,Y≧1)=P(Y≧1) 這個應該沒問題 P(X≧1,Y≧1)≦P(X≧1)≦E(X)且P(X≧1,Y≧1)≦P(Y≧1)≦E(Y) 所以P(X≧1,Y≧1)小於E(X),E(Y)中的最小值 => P(X≧1,Y≧1)≦min( E(X),E(Y) ) --

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