How to represent E(Y|X) in terms of E(X), E(Y), Var(X), Cov(X,Y)? Known things are:
E(Y|X)=aX+b, 
Cov(X,Y) exists,
0 < Var(X) < Infinity,
Question:
Represent a,b in terms of E(X), E(Y), Var(X), Cov(X,Y)
I worked out only one equation: E[E(Y|X)]=E(Y)=E(aX+b)=aE(x)+b, i.e. aE(X)+b=E(Y).
But in order to represent a and b another equation is needed.
Please help me, thanks~

Hint: You already worked out half of the answer:
$$E[E(Y|X)]=E(Y)=E(aX+b)=aE(x)+b \implies  aE(X)+b=E(Y)$$ 
Additionally:
$$E [X \, E [Y|X] =E[E[X Y |Y]]=E[XY]=Cov(X,Y)+E[Y][X]$$
but
$$E [X \, E [Y|X]] =E[X (aX+b)]=a E[X^2]+b E[X]=a (Var(X)+E[X]^2)+b E[X]$$
Combining these two equations, and together with the one above, you can get $a$ and $b$
