What are the PDFs of multivariate continuous Gaussian random vectors?

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Let, $X_{i}$ is a vector of random variables, where $i= 1,2,3,...,n$.

$1$. What would be $PDF(x)$, if $X_i$ is dependent?

$2$. What would be $PDF(x)$, if $X_i$ is independent?

$3$. What would be $PDF(x)$, if $X_i$ is Parzen?


N.B. I only need correct formulas. Coz, I am confused with so many varieties of them.