# Questions tagged [joint-distribution]

Joint probability distribution of several random variables gives the probability that all of them simultaneously lie in a particular region.

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### Shouldn't the joint probability of 2 independent events be equal to zero?

If the joint probability is the intersection of 2 events, then shouldn't the joint probability of 2 independent events be zero since they don't intersect at all? I'm confused.
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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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### Upper bounds for the copula density?

The Fréchet–Hoeffding upper bound applies to the copula distribution function and it is given by $$C(u_1,...,u_d)\leq \min\{u_1,..,u_d\}.$$ Is there a similar (in the sense that it depends on the ...
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### Uncorrelatedness + Joint Normality = Independence. Why? Intuition and mechanics

Two variables that are uncorrelated are not necessarily independent, as is simply exemplified by the fact that $X$ and $X^2$ are uncorrelated but not independent. However, two variables that are ...
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### Maximum of a probability vector distributed as a Dirichlet variate

Let $p_1, p_2, \ldots \sim \text{Dirichlet}(\alpha_1, \alpha_2, \ldots)$. What is the distribution of $\max(p_1, p_2, \ldots)$? I have searched for the order statistics of the Dirichlet distribution ...
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### Question about joint distribution of Bernoulli random variables under constraint that sum must be 1

I am stuck with a problem at work. Can anybody please help me to give me the joint distribution of $n$ Bernoulli random variables but under the constraint that the sum of the these $n$ random ...
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### Exchangeability and joint distribution

The definition of an exchangeabilty for a finite sequence says that, if we have random variables $X_1,\ldots,X_n$, then for each permutation $\pi: \{1,\ldots,n\}\rightarrow\{1,\ldots,n\}$, the joint ...
Given two continuous random variables $X$ and $Y$, the joint cumulative distribution function $F_{X,Y}$ is defined as F_{X,Y}(x,y)=\mathbb{P}(X\le x, Y\le y)=\displaystyle\int_{-\infty}^{x}\int_{-\...