Linked Questions

94
votes
4answers
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 ...
3
votes
1answer
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 ...
2
votes
1answer
1k views

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 ...
2
votes
1answer
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 ...
1
vote
2answers
106 views

Distribution for an operation of variables with identical distributions

I have this doubt: Consider $X$~$N(\mu_X,\sigma^2)$, $Y$~$N(\mu_Y,\sigma^2)$ and $Z=X-Y$ I know that $E(Z)=E(X)-E(Y)=\mu_X-\mu_Y$ because the expected value is a linear operator. And I know that $...
1
vote
1answer
158 views

Why do I need multivariate normality tests?

I am new to time series analysis and would like to test a multivariate time series (12 components) for normality. I found several straightforward normality tests and some multivariate normality tests. ...
1
vote
1answer
69 views

What is the probability that two data points in a normally distributed data set have the same value?

How does one determine the probability that two data points have the same value, given the data set is normally distributed and how does the actual value of these points influence this probability?
0
votes
0answers
64 views

If I have two random variables, $X_1, X_2 \sim N(\mu, \sigma^2)$, what can I say about $X_1-X_2$? [duplicate]

If I have two random variables, $X_1, X_2 \sim N(\mu, \sigma^2)$ where $\mu, \sigma^2$ are unknown, what can I say about $X_1-X_2$? More specifically, I know that the difference should be a normal as ...
5
votes
0answers
48 views

An example of a bivariate distribution with normal marginals and a nonlinear conditional mean curve? [duplicate]

That is, an example of a bivariate distribution with normal marginals for which a linear regression is inappropriate. Does an asymmetric copula always produce this?
0
votes
0answers
17 views

Gaussian Distribution [duplicate]

Assume we have two continuous Normal RV "X" and "Y". how can I show the conditional PDF f(X|Y) and f(Y|X) is Normal?