Let X and Y be jointly continuous random varibles with joint density( ) , the conditional probability that X lies between 0 and (1/2) givenX<Y .

根据题意，需要求解条件概率 P(X<1/2|X<Y)。可以使用全概率公式和条件概率公式来求解：

P(X<1/2|X<Y) = P(X<1/2,X<Y) / P(X<Y)

由于 X 和 Y 是联合连续随机变量，可以使用二重积分来计算概率：

P(X<1/2,X<Y) = ∫[,1/2]∫[x,1] f(x,y) dy dx

P(X<Y) = ∫[,1]∫[,y] f(x,y) dx dy

将上述积分带入公式中，即可求解条件概率。

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