Finding the density of Y~N(µ,V)

Finding the density of Y~N(µ,V)

Can anyone explain to me how to go about finding the density for a normally distributed multivariate function Y~N(µ,V), where Y is nonsingular and V is a positive definite? Thanks!

welkie said:

Can anyone explain to me how to go about finding the density for a normally distributed multivariate function Y~N(µ,V), where Y is nonsingular and V is a positive definite? Thanks!

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If by density you mean probability of being between Y and (Y+dY), it is

\(\displaystyle \displaystyle f(Y)\ dY = \dfrac{1}{\sqrt{2\ \pi\ V}}e^{-(x-\mu)^2/(2\ V)}\ dY\)

This is usually written with standard deviation \(\displaystyle \sigma=\sqrt{V}\) instead of \(\displaystyle V\)

\(\displaystyle \displaystyle f(Y)\ dY = \dfrac{1}{\sqrt{2\ \pi}\ \sigma}e^{-(x-\mu)^2/(2\ \sigma^2)}\ dY\)