Linked Questions

5
votes
1answer
4k views

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 ...
8
votes
0answers
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 ...
6
votes
3answers
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 ...
1
vote
1answer
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?
1
vote
0answers
54 views

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 ...
0
votes
0answers
46 views

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 $ρ_{xz}=0.87$ ...
0
votes
0answers
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...
1
vote
0answers
40 views

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 ...
0
votes
0answers
29 views

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
0
votes
0answers
19 views

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 ...
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?
25
votes
5answers
2k views

Introductory reading on Copulas

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 ...
18
votes
4answers
673 views

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 ...
10
votes
4answers
9k views

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 ...
15
votes
5answers
4k views

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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