Is this formula true? $P(X<Y | Y = y) = P(X<y)$
I am trying to solve this with conditional formula, but don't know how
$P(X<Y | Y= y) = \frac{P(X<Y, Y= y)}{P(Y=y)} = \frac{P(X<y)}{P(Y=y)}. $
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2Are $X$ and $Y$ independent? – Mankind Nov 13 '18 at 17:12
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suppose it is independent, then P(X<Y,Y =y) = P(X<Y)P(Y=y) gives P(X<Y) which is still not P(X<y) – Zewen Huang Nov 15 '18 at 06:19