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Homework Statement
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-0.25 <= P( X [tex]\cap[/tex] Y ) - P( X )P( Y ) <= 0.25
for any events X, Y
Homework Equations
P( X [tex]\cap[/tex] Y ) = P( X )P( Y | X )
Bayes' theorem
Anything I missed?
The Attempt at a Solution
Obviously if X and Y are independent
P( X [tex]\cap[/tex] Y ) = P( X )P( Y )
so
P( X [tex]\cap[/tex] Y ) - P( X )P( Y ) = 0
but if they are not then I hit a wall. I've done pages of math but I go round in circles. I think there's some trick but I can't figure it out. Can anyone tell me what I'm missing?