Suppose that X and Y are random variables such that E(Y/X)=aX+b,how determine expressions for a and b in terms of E(X),E(Y),Var(X),and Cov(X,Y).assuming that Cov(X,Y) exists and Var(X)>0.
Using the tower property, recall that $E[E[Y|X]] = E[Y]$. You should try to work that out in order to obtain an equation in terms of $E[X]$ and $E[Y]$,
Also, recall that $Cov(X,Y) = E[XY] - E[X]E[Y]$. Hence you can try to write $E[XY]$ in terms of $Var[X]$ and $E[X]$ to get another equation. Recall that $E[XY] =E[E[XY|X]] = E[X \cdot E[Y|X]]$,
Using this expression, obtain:
Finally, you can obtain the desired relation solving for $a$ and $b$ using the two equations.