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)}. $
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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