Linked Questions

4
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
220 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
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?
1
vote
0answers
47 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
42 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 $ρ_{xz}=0.87$ ...
1
vote
0answers
38 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
14 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 ...
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
639 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 ...
10
votes
3answers
3k views

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://...
14
votes
3answers
930 views

Can a 3D joint distribution be reconstructed by 2D marginals?

Suppose we know p(x,y), p(x,z) and p(y,z), is it true that the joint distribution p(x,y,z) is identifiable? I.e., there is only one possible p(x,y,z) which has above marginals?
12
votes
2answers
1k views

Are normally distributed X and Y more likely to result in normally distributed residuals?

Here the misinterpretation of the assumption of normality in linear regression is discussed (that the 'normality' refers the the X and/or Y rather than the residuals), and the poster asks if it is ...

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