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## Homework Statement

Let Xn be a sequence of p dimensional random vectors. Show that

Xn converges in distribution to [tex]N_p(\mu,\Sigma)[/tex] iff [tex]a'X_n[/tex] converges in distribution to [tex]N_1(a' \mu, a' \Sigma a).[/tex]

## Homework Equations

## The Attempt at a Solution

[tex]E(e^{(a'X_n)t} = E(e^{(a't)X_n}) = e^{a't \mu + 0.5t^2(a' \Sigma a)}[/tex]

Hence, {a'Xn} converges [tex]N(a' \mu, a' \Sigma a).[/tex] in distribution.

Is that it?