Let Ω=[0,1], B(Ω) the Borel Sigma algebra and Leb the Lebesgue measure on Ω.

Question

Let's say that X Is a random variable defined under (Ω,B(Ω),Leb) And Y: Ω->R Is given by: Y(w)=w(1-w)1Ω(w) Determinate E(X|Y)(w)for each w that belongs to Ω.

I've been going through some probability problems and I got stuck in this one, I hope you guys can help me.