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### Is a vector of normal random variables ever -not- multivariate normal [duplicate]

Possible Duplicate: Is it possible to have a pair of Gaussian random variables for which the joint distribution is not Gaussian? In the Wikipedia entry on the multivariate normal distribution, it ...
7k views

### When are two normally distributed random variables jointly bivariate normal? [duplicate]

Possible Duplicate: Is it possible to have a pair of Gaussian random variables for which the joint distribution is not Gaussian? For our upcoming exam we had to calculate the joint density of two ...
197 views

### When are correlated Normal random variables multivariate Normal? [duplicate]

I know that there are many example of correlated normal random variables which are not jointly (multivariate) normal. However, are there conditions which state when correlated normal random variables ...
222 views

### Is it possible for $X$ and $Y$ to be marginally normally distributed and have $E[Y|X]$ be a nonlinear function of $X$? [duplicate]

Is this at all possible? What is the intuition for this?
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### Deriving the Bivariate Normal Distribution from Normal Distributions [duplicate]

If $X \sim N(0,{a^2})$, $Y \sim N(0,{b^2})$ and $Corr(X,Y) = \rho$, then can we say that $(X,Y) \sim BVN(0,0,{a^2},{b^2};\rho )$? If this is true, then can someone please tell me how can I ...
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### What do the joint distributions look like? [duplicate]

I know that if I know the marginal distributions, that's not enough to specify the joint distribution. But obviously it can't be "any" joint distribution, it still needs to respect its marginal ...
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### correlation coefficient bivariate normally distributed [duplicate]

Suppose that X,Y and X,Z are bivariate normally distributed. We have $E(X)=0, Var(X)=10$, $E(Y)=0, Var(Y)=6$ and $ρ_{xy}=0.87$ Moreover, $E(X)=0, Var(X)=10$, $E(Z)=0, Var(Z)=4$ and $ρ_{xz}=0.87$ ...
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### symmetric marginal but asymmetric joint distribution contours [duplicate]

Let us say we have two continuous random variables, $X$ and $Y$ such that their pdfs $f(x)= f(-x)$ and $g(y)= g(-y)$ for all $x$ and $y$. In other words, $X$ and $Y$ have symmetric distributions ...
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For some time now, I have been looking for a good introductory reading on Copulas for my seminar. I am finding lots of material that talk about theoretical aspects, which is good, but before I move ...
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### What is the intuition behind the independence of $X_2-X_1$ and $X_1+X_2$, $X_i \sim N(0,1)$?

I was hoping someone could propose an argument explaining why the random variables $Y_1=X_2-X_1$ and $Y_2=X_1+X_2$, $X_i$ having the standard normal distribution, are statistically independent. The ...
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### Can somebody illustrate how there can be dependence and zero covariance?

Can somebody illustrate, as Greg does, but in more detail, how random variables can be dependent, but have zero covariance? Greg, a poster here, gives an example using a circle here. Can somebody ...
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### Difference between the terms 'joint distribution' and 'multivariate distribution'?

I am writing about using a 'joint probability distribution' for an audience that would be more likely to understand 'multivariate distribution' so I am considering using the later. However, I do not ...
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### Should Dirac's delta function be regarded as a subclass of the Gaussian distribution?

In Wikidata it is possible to link probability distributions (like everything else) in an ontology, e.g., that the t-distribution is a subclass of the noncentral t-distribution, see, e.g., https://...