Timeline for How to show that two linear combinations of Bernoulli random variables have jointly Gaussian distribution (and more)

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Dec 15, 2014 at 11:29	comment	added	TOM		And, if, say, I rescale them, is there a corresponding Berry-Esseen bound available (proved in some paper)?
Dec 15, 2014 at 10:23	history	edited	TOM	CC BY-SA 3.0	edited body
Dec 15, 2014 at 10:23	comment	added	TOM		zhoraster: thank you! The answer to #1 is very helpful. I am not sure why it is not true for #2. Say $f,g$ are both bounded and continuous, or, if necessary - Lipschitz, why would discreteness matter? I would see why it would fail for "bump" functions that look like an indicator of a very short interval, but what about polynomials of fixed degree?
Dec 14, 2014 at 12:56	comment	added	zhoraster		1) Using Carmer-Wold criterion and Lyapunov CLT it is easy to show that $(Xn^{-1/2},Yn^{-3/2})$ converges to a centered Gaussian vector with covariance matrix $\begin{pmatrix} 1 & 1/2\\ 1/2 &1/3 \end{pmatrix}$. 2) No, because $X$ and $Y$ are integer valued. If, however, you scale them, then the convergence would follow from the CLT.
Dec 14, 2014 at 9:12	history	edited	TOM	CC BY-SA 3.0	added 1 character in body
Dec 13, 2014 at 13:55	history	asked	TOM	CC BY-SA 3.0