Consider the matrix : $$M=\begin{pmatrix} 1& 0& \mu_2 \\ 0& \mu_2& \mu_3 \\ \mu_2& \mu_3& \mu_4 \end{pmatrix}$$ where $\mu_k$ denotes the $k^{th}$ central moment of a RV X i.e. $\mu_k := E(X-E(X))^k$.
Prove that:
(a) $M$ has non-negative determinant.
(b) $M$ is non-negative definite.
(c) Generalize this result to higher dimensions.
My thoughts:
(a) I tried to break the moments to lower order moments and to obtain the result but it didn't workout.
(b) & (c) Could not come up with anything.