# 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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### Conditional cdf

I want to know that how conditioning will affect the CDF of dependent random variables. More specifically, let's suppose, $\Gamma_R={g\over A}$ and $\Gamma_D={g\cdot h\over B}$, where $g$ and $h$ are ...
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### Maximum likelihood estimation (MLE) for a Bayesian network with binary variables

I have below Bayesian network of 4 variables A, B, C, and D. All variables are binary except D, which is real-valued. $P(A|B,C)$ is defined by the conditional probability table (CPT) on the right. ...
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### How to find $\mathbb{P}(X<C)$ where both $X$ and $C$ are RVs and $X$ depends on another RV?

I have a scenario like the following: $C$ is a random variable that follows $\operatorname{Uniform}(0, 3.5)$. $T$ is a random variable with $\operatorname{Exponential}(\operatorname{mean}=3)$ for ...
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### should the product of 2 independent binomials converge to a normal distribution for large sample sizes?

I have been studying 2x2 contingency tables and specifically I have been looking at situations where the marginals are fixed by design for one categorical variable. As an example, suppose a ...
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### Independence of ordered statistics part 2

In relation to my previous question, I have a second problem. How to show that $U_1+U_2$ is independent of $Y_3$? I can find out the pdf of $U_1+U_2$, as well as of $Y_3$, however please help me ...
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### What are the values of output $g_i$ in Bengio's paper “Taking on the Curse of Dimensionality in Joint Distributions Using Neural Networks”

Figure 2 of Bengio's paper "Taking on the Curse of Dimensionality in Joint Distributions Using Neural Networks" describes a neural network structure for estimating a joint probability distribution. ...
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### how to find asymptotic joint distribution of two linear combination of order statistics?

Suppose I have n order statistics from some unknown continuous distribution funciton F(x), $X_{1}\leqslant X_{2}\leqslant...\leqslant X_{n}$. And I have two linear combination of these order ...
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### Distribution of ratio of two independent normal variables

My objective is to find out the distribution of $A/B$ given $A \sim N(a,b); B \sim N(c,d)$. I set $Z_1$ equal to $\frac{(A-a)}{\sqrt{b}}$ and $Z_2$ equals $\frac{(B-c)}{\sqrt{d}}$ such that $Z_1$ ...
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### Calculate mutual information of twitter's users interactions

I have a research project about finding out user's interaction on Twitter. If I want to calculate the mutual information between two users A,B: I(A,B), to know the probability of A and B appearing in ...
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### Estimating a joint distribution from observed max and min samples

Suppose that you have jointly distributed $N$ (~100) random variables, $\{X_1,\ldots,X_N\}$, and this distribution is unknown to you. However you do know that their sum is zero by construction. Having ...
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### Does relative Kullback-Leibler divergence exist?

Suppose I have two multivariate normal distributions. I have computed the KL divergence ($d_{KL}(N_1, N_2)$). Is there a way to measure a relative divergence between these two distributions? For ...
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### Jensen–Shannon divergence relation between marginal and joint

I have the following distributions- Joints: $p_1$(x,y) = $\rho_1$(x) $q_1$(y|x), $p_2$(x,y) = $\rho_2$(x) $q_2$(y|x) And the marginals: $\rho_1$(x), $\rho_2$(x). Is it possible to provide any ...
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