30k views

### Is it possible to have a pair of Gaussian random variables for which the joint distribution is not Gaussian?

Somebody asked me this question in a job interview and I replied that their joint distribution is always Gaussian. I thought that I can always write a bivariate Gaussian with their means and variance ...
4k views

### Same Joint Distribution, different conditional and marginal distribution

I have a group of samples drawn from density function $p(x,y)$, so it has the marginal density $p(x)$ and $p(y)$, and conditional density $p(x|y)$ and $p(y|x)$. In what way I can construct another ...
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### Are marginals of a jointly Gaussian sequence always Gaussian?

Are marginal distributions of the random variables comprising a jointly gaussian random vector always Gaussian? This stems from my confusion with the Central Limit Theorem which loosely states that ...
960 views

### Joint probability density function

I'm stuck with this question: Suppose I have two random variables: A and B such that $$A\sim N(\mu_A,\sigma_A)$$ $$B\sim N(\mu_B,\sigma_B)$$ A and B are independent. I create a new random variable ...
106 views