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### Gaussian random variables [duplicate]

Can some one help me point in the right direction or point to some resources that will help me prove that sum of two jointly distributed Gaussian r.v. with a given correlation coefficient is also a ...
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### How to compute a probability threshold for a linear combination of two variables ~ N(0,1)?

I have a variable which is a linear combination of two other variables, each one following an N(0,1) distribution. I need to compute the threshold of the distribution of this combination variable (to ...
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### Generate identically distributed dependent normal random numbers with prespecified sum

How do I generate $n$ identically distributed but not independent normal random numbers such that their sum falls within a prespecified interval $[a,b]$ with probability $p$? (This question is ...
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### Is the joint distribution of two linear combinations of Gaussians still a multivariate normal?

Suppose I have $\textbf{X}$ ~ $N(\textbf{0},\Sigma)$, and I'm considering two different linear combinations, $a^* X$ and $b^* X$, which we suppose are uncorrelated. I understand that linear ...