Hey guys. I am going through the PRM (risk manager) material and there is a sample question that is bugging me. The PRM forum is relatively dead, and they don't usually go that deep into the theory anyway. So wanted to ask you guys.(adsbygoogle = window.adsbygoogle || []).push({});

Shouldn't a random vector always have a covariance matrix? Why is the "answer" below saying that it doesn't always have to exist? i.e. why is (c) wrong?

Q: A covariance matrix for a random vector:

a) Is strictly positive definite, if it exist

b) Is non-singular, if it exist

c) Always exists

d) None of the above

A: This question is full of red herrings. A covariance matrix may not exist, which contradicts c). If it does exist, it is in general only positive semi-definite, which contradicts both a) and b) hence d).

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# Covariance matrix does not always exist?

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