Let X and Y be jointly distributed as BN(1,0,36,16,1/2). Consider the following statements: I. E(Ymid X=7)=2 II. Cov(X+Y, Y-X)=-20 III. V(Xmid Y=1)=27 Which of the statements given above are correct?

Q36Section I (Objective (Q1–Q80))36 of 79

Distribution Theory — conditional and covariance properties in bivariate normal

Let $X$ and $Y$ be jointly distributed as $BN(1,0,36,16,1/2)$ . Consider the following statements:

$\text{I. } E(Y\mid X=7)=2$

$\text{II. } \operatorname{Cov}(X+Y, Y-X)=-20$

$\text{III. } V(X\mid Y=1)=27$

Which of the statements given above are correct?

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