Are X and Y dependent random variables?

[docnet]

Homework Statement

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Relevant Equations

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(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.

 

[Orodruin]

Look fine