Have $(U,V)$ be a pair of Bivariate Gaussian variables with mean $0$, variance $1$ and $Cov(U,V) = p$ where 0 < ρ < 1

Asked Jun 07 '19 at 14:22

Active Jun 07 '19 at 14:27

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Have $(U,V)$ be a pair of Bivariate Gaussian variables with mean $0$, variance $1$ and $Cov(U,V) = ρ$ where $0 < ρ < 1$

I'd like help finding the density of $U+V$

So far I have tried to use $P(U+V<=t) = E(P(U+V<=t | V))$ but a am not having much success in advancing. Any help would be appreciated.

Note: This is not a homework problem, but a problem I am doing to help study.

asked Jun 07 '19 at 14:22

Jay

Because these are bivariate Gaussian, their sum is univariate Gaussian, whence the only information needed to completely characterize it is its mean and variance: compute them. – whuber Jun 07 '19 at 14:26
1

Sorry this is a duplicate, should I delete my question? I was thrown off by the use of Gaussian instead of normal. – Jay Jun 07 '19 at 14:37

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