Q156·Section III (Statistics)·156 of 180Bivariate normal — shape of the conditional mean and varianceSuppose (XY)∼\left(\begin{smallmatrix}X\\Y\end{smallmatrix}\right)\sim(XY)∼ Bivariate Normal (μ‾2×1,Σ2×2)(\underline\mu_{2\times1},\Sigma_{2\times2})(μ2×1,Σ2×2). Then: OptionsAE(Y∣X=x)=x E(Y)E(Y\mid X=x)=x\,E(Y)E(Y∣X=x)=xE(Y)BVar(Y∣X=x)=x2Var(Y)\operatorname{Var}(Y\mid X=x)=x^2\operatorname{Var}(Y)Var(Y∣X=x)=x2Var(Y)CE(Y∣X=x)=E(Y)+aE(Y\mid X=x)=E(Y)+aE(Y∣X=x)=E(Y)+a linear function of xxxDVar(Y∣X=x)=Var(Y)+a\operatorname{Var}(Y\mid X=x)=\operatorname{Var}(Y)+aVar(Y∣X=x)=Var(Y)+a quadrate function of xxxPick an option to check your answer.Show answerShow solution Report a problem with this question← Q155All questionsQ157 →Keyboard: A–D answer · S solution · ←/→ previous/next