# Expectation and Eigenvalues, Statistics question watch

1. Hello,
I was wondering if someone could help me with this ?
I’ve been trying to do this question but not seeming to get anywhere, I’m guessing it’s something relatively simple?
Thanks for any help
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2. Well just look at what the diagonal of the covariance matrix is. Then think about how you can simplify that when you know that for i =1,..,p, E(X_i) = 0. Then it should just follow from linearity of expectation when setting X = (X_1 .... X_p).

The second equality is just linear algebra, it applies to a general matrix with entries in R, that trace is equal to sum of eigenvalues. One way you can show this uses det(AB)=det(A)det(B) and that S is symmetric (so diagonalisable).

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Updated: February 7, 2018
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