# Thread: Distribution of X+Y of a bivariate normally distributed (X,Y)

1. ## Distribution of X+Y of a bivariate normally distributed (X,Y)

I need to give the distribution of $X+Y$ and $X-Y$ knowing that $(X,Y)$ is bivariate normally distributed with marginal means 1, marginal variances 1 and correlation $p=2$.Is it right that the marginal mean are simply $E(X)=1$ and $E(Y)=1$ ?I don't see where I should start knowing that.

2. ## Re: Distribution of X+Y of a bivariate normally distributed (X,Y)

First of all, when you are talking about random vector, its mean is also a vector of the same dimension. In the context it seems to indicate that both and has a marginal mean of , or equivalently the mean vector and so you should be correct. The marginal means are just the corresponding components in the mean vector.

One more thing is that the correlation is a bounded quantity in . So the correlation cannot be . Moreover, since the marginal variances are too, so the absolute value of covariance , i.e. also bounded by

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