Question: 1. Consider a bivariate normal random vector X = (X1,X2)' with E(X) = = (0 2)', Var(X1) = 2, Var(X2) = 5, and correlation coefficient

1. Consider a bivariate normal random vector X = (X1,X2)' with E(X) = = (0 2)',

Var(X1) = 2, Var(X2) = 5, and correlation coefficient Corr(X1,X2) = 0.3.

(a) Draw a contour A ={f(x1, x2) : f(x1,x2) = 0.03} for the bivariate normal density.

(b) What are the loading vectors v1 and v2 of the principal components for X? Add loading

vectors v1 and v2 to the plot in (a) with starting point at .

(c) What are the standard deviations of principal components for X? What is their relation

with the lengths of the major and minor axes of the ellipse A?

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