1. Let Yo, Yı,..., Y, be independent and identically distributed random variables with mean 0 and variance o2. Define X;
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1. Let Yo, Yı,..., Y, be independent and identically distributed random variables with mean 0 and variance o2. Define X; = Y+Y; i=1(1)p. (a) Show that there is a principal component of X = (X1,..., XP)' that is proportional to X = X-X. (b) Show that the above principal component is in fact the first principal component.