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I do not understand the below definition for the bivariate normal...

Up (formula 4-5) is defining the squared distance as a function of 2 variables $x_1$ and $x_2$.

And below(formula 4-6) is the full formula.

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How does that "2" makes it to the final formula if it clearly wasn't part of the squared distance?

I know it says "the expression for the bivariate (p=2)", but in (4-5) is also doing it for p=2.

I pointed with an arrow the "2" appearing in the final formula and where it should appear in the squared distance. Which one is wrong? or what am I missing?

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The density of a $k$-variate random variable with normal distribution has the form: $$ f(x) = \frac{1}{\sqrt{(2\pi)^k|\Sigma|} } exp(-\frac{1}{2}(x-\mu)' \Sigma^{-1} (x-\mu)) $$

The term $-\frac{1}{2} $ comes from the definition, not from the computation of $(x-\mu)' \Sigma^{-1} (x-\mu)$.

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