Are X and Y dependent random variables?

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Homework Statement
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Relevant Equations
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Screen Shot 2021-12-09 at 3.31.44 AM.png
Screen Shot 2021-12-09 at 3.34.30 AM.png

(a) the agrea of the triangleses is 1, so γ one.

(b) I'm not sure how to prove. i feel like ##X## and ##Y## are dependent because ##E(Y|X=0)=\frac{1}{2}## and ##E(Y|X=1)=0## so ##Y## seems dependent on ##X##. ##f_X=1-x## for ##x>0## ane ##f_X=1+x## for ##x<0## so X seems independent on Y.
 
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