Are X and Y dependent random variables?

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The discussion revolves around the dependency of random variables X and Y. It is noted that the expected value of Y given X shows a dependency, as E(Y|X=0) equals 1/2 and E(Y|X=1) equals 0. However, the probability density functions suggest that X is independent of Y, with f_X being defined differently for positive and negative values of x. This creates a contradiction in the assessment of their dependency. The conclusion remains unclear, highlighting the complexity of determining the relationship between X and Y.
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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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