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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 ...
413 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 ...
227 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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### 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 $ρ_{xz}=0.87$ ...
46 views

### vector of three RVs that are pairwise Gaussian is Gaussian [duplicate]

If $(X,Y)$, $(X,Z)$, and $(Y,Z)$ are all Gaussian, does it follow that $(X,Y,Z)$ is also Gaussian? I'm having trouble coming up with a counterexample...
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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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### variables that are normaly distributed but their joint distribution is not multivariate normal with ρ = 0.5 [duplicate]

can you give me an example or explain me how to find one. It can be with copulas
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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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### 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?
2k views

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 ...