Let $ \{ \xi_n \}_{n=1}^{\infty}$ be a sequence of normal random variables, where $ \xi_n\sim\mathcal{N}(\alpha_n, \sigma_n^2)$ and $\xi_n \overset{d}{\rightarrow} \xi$. I need to prove, that $\xi$ is also a normal random variable, can anyone help?
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3Use characteristic functions. – Did Jan 20 '13 at 21:01
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@Stefan: That's part of the conclusion. – cardinal Jan 20 '13 at 21:14