Conditional expected value on iid variables

[animalknox]

Let (Xi) i=1 to 3 be independent identically distributed random variables, each following the distribution P(Xi = 0) = 1/2 = P(Xi = 1)
Consider the random variable Y = max (Xi )and Z = Sum(Xi)
Calculate the following quantities E(|E(X1|Y )|^2)

I can find the probability laws of Y and Z -> P(Y=0)=1/8 and P(Y=1)=7/8, P(Z=0)=1/8=P(Z=3) and P(Z=1)=3/8=P(Z=2) but after I don't know what it enables me to do, I think there's a relation between expected value squared and probability that I must have missed in the lecture. Could someone help me out ?

 

[tkhunny]

Have you yet produced the first result?

What is E[X1|Y]?