Let X=(X1,X2,X3)^T be a 3times1 random vector with E(X)=(3,2,1)^T and Cov(X)=Sigma=beginpmatrix3 & -2 & 0 -2 & 3 & -2 0 & -2 & 3endpmatrix. Suppose that Y=(Y1,Y2,Y3)^T=1/sqrt3X. Then the value of the multiple correlation coefficient between Y1 and (Y2,Y3) equals

Q58Section B (Part B)58 of 120

Multivariate analysis — a multiple correlation coefficient

Let $X=(X_1,X_2,X_3)^{T}$ be a $3\times1$ random vector with $E(X)=(3,2,1)^{T}$ and

$\operatorname{Cov}(X)=\Sigma=\begin{pmatrix}3 & -2 & 0\ -2 & 3 & -2\ 0 & -2 & 3\end{pmatrix}.$

Suppose that $Y=(Y_1,Y_2,Y_3)^{T}=\frac{1}{\sqrt3}X$ . Then the value of the multiple correlation coefficient between $Y_1$ and $(Y_2,Y_3)$ equals

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