Let (omega,F,P) = ([0,1), Borel, Lebesgue). For n = 0,1,2,3,...

let Qn=sigma([k/2^n, (k+1)/2^n) : 0 =< k < n) be the dyadic partitions of[0,1).

Let X(s)=s, 0=< s < 1.

a) Find the equation of and sketch E(X|Q0), E(X|Q1) and E(X|Q2).

b) Let Yn=E(X|Qn). Show that E(Y6|Q4)=Y4. Find E(Y4|Q6).

This is very difficult to me. I cant solve it. please help me...