$ {y}_{\rm MMSE}(x) \int\limits_{-inf}^{inf}\ {y}{f}_{\rm y|x}(Y|X=x)\, dy={E}(Y|X=x) $
$ {y}_{\rm LMMSE}(x)=E[\theta]+\frac{COV(x,\theta)}{Var(x)}*(x-E[x]) $
Mean square estimate : $ MSE = E[(\theta - \hat \theta(x))^2] $
