3. Let X = (X1,..., Xm)', m > 2, be random vector with covariance matrix s-[] O 12 Σ O21 222 The multivariate correlation coefficient between X1 and X2, .., Xm, denoted R1.2.m; the maximum correlation between X1 and any linear function W2X2+ (i) Show that + Wm Xm. ... 1/2 (ii) Suppose that random vector X has multivariate normal distribution. Show that R1.2,.m is equal to the correlation between X1 and E[X1|X2, ..., Xm].

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