# Tag Info

## Hot answers tagged joint-distribution

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

There is a difference between independent events: $\mathbb P(A \cap B) =\mathbb P(A)\,\mathbb P(B)$, i.e. $\mathbb P(A \mid B)= \mathbb P(A)$ so knowing one happened gives no information about ...
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### Why don't we see Copula Models as much as Regression Models?

The first and most important reason is that standard regression models had a one to two-hundred year headstart on copula models (depending on exactly where you count the genesis of regression models ...
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### Proof that joint probability density of independent random variables is equal to the product of marginal densities

By definition, the random variables $X_1,\dots,X_n$ are independent iff $$\Pr(X_1\in B_1,\dots,X_n\in B_n) = \Pr(X_1\in B_1)\dots\Pr(X_n\in B_n)$$ for every choice of Borel sets $B_1,\dots,B_n$. ...
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### intuitive difference between joint probability and conditional probability in this example

You actually had your answer right there. $P(H=hit)$ is the marginal probability. It reads "The probability of getting hit.". It is the proportion of people that got hit crossing the street, ...
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### Why don't we see Copula Models as much as Regression Models?

A reason might be that regression and copulas do not answer the same question. Copulas are about the joint distribution while regression is about a conditional distribution or just the conditional ...
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### Shouldn't the joint probability of 2 independent events be equal to zero?

What I understood from your question, is that you might have confused independent events with disjoint events. disjoint events: Two events are called disjoint or mutually exclusive if they cannot ...
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### Joint distribution in layman's terms

As a concrete example, suppose I toss a coin and roll a die one after the other. As you know, there is a probability distribution associated with the outcomes of both (discrete uniform distributions, ...
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### Minimum CDF of random variables

Let $x$ by any number. Consider the event $\min(X,Y)\le x$. It can be expressed as the union of two events $$\min(X,Y)\le x = (X\le x) \cup (Y \le x),$$ shown by the overlapping yellow and green ...
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### What is the number of parameters needed for a joint probability distribution?

It takes $3\times 2 \times 2 \times 3 = 36$ numbers to write down a probability distribution on all possible values of these variables. They are redundant, because they must sum to $1$. Therefore ...
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### Joint probability measure

Joint Distributions and Expectation In general, the joint distribution of random variables $X$ and $Y$, defined on a common probability space $(\Omega, \mathcal{A}, \mathbb{P})$ and taking values in ...
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### Why don't we see Copula Models as much as Regression Models?

A short answer is that in practice for many applications we don't need the joint probability distributions. A cynic would say that it's also because the users don't event understand what is a joint ...
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### Difference between joint density and density function of sum of two independent uniform random variables

Following up on Glen_b's answer, and in an attempt to dumb it down a bit more, the following illustrations shows how the bivariate or joint pdf of $X$ and $Y$, both independent and standard uniform ...
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### Derivative of the Joint Distribution Interpretation

The first-order partial derivatives of a multivariate joint distribution function can be considered as giving the density of the differentiated variable, jointly with the cumulative probability of the ...
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All of these DGPs generate a standard bivariate Gaussian with: $$\begin{pmatrix} X \\ Y \end{pmatrix}\sim N\left(\begin{pmatrix} 0 \\ 0 \end{pmatrix},\begin{pmatrix} 1 & \sigma_{xy} \\ \sigma_{xy}... • 12.7k 9 votes Accepted ### What does it mean to factor a joint distribution? If I am understanding the passage and table correctly, there are essentially two answers: mathematical and qualitative. Qualitatively, the "different aspects of forecast quality" is essentially the ... • 13k 9 votes Accepted ### Maximum of a probability vector distributed as a Dirichlet variate I am not sure there is a closed-form solution for the distribution of p_{(k)} when (p_1,\ldots,p_k)\sim\text{Dir}(\alpha_1,\ldots,\alpha_k) and the \alpha_i's are different. At least, it ... • 107k 9 votes Accepted ### Distribution given sum It can be instructional and satisfying to work this out using basic statistical knowledge, rather than just doing the integrals. It turns out that no calculations are needed! Here's the circle of ... • 328k 9 votes ### How to make random draws from an unspecified distribution? Presumably w_1+w_2=1 and w_1,w_2 \geq 0, so f is a convex combination of f_1,f_2 and therefore a valid distribution (a mixture of f_1,f_2). Generate a Bernoulli(w_1) random variable (i.e. ... • 636 9 votes Accepted ### Uncorrelatedness + Joint Normality = Independence. Why? Intuition and mechanics The the joint probability density function (pdf) of bivariate normal distribution is:$$f(x_1,x_2)=\frac 1{2\pi\sigma_1\sigma_2\sqrt{1-\rho^2}} \exp\left[-\frac z{2(1-\rho^2)}\right], $$where$$z=\...
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Some hints: Geometrical approaches are much easier for uniform RVs, but the general approach is to integrate the joint PDF in the region that satisfy $XY>\alpha$. The integral will basically look ...