# Questions tagged [joint-distribution]

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

157 questions
188 views

117 views

156 views

### 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 ...
738 views

### 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. ...
42 views

### 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 ...
101 views

### 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 ...
25 views

### 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 ...
28 views

### 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. ...
133 views

### 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 ...
228 views

### 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 $Z_1$ ...
54 views

### 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 ...
87 views

### 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 ...
191 views

### 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 ...
1k views

I want to show that $$\newcommand{\cov}{\operatorname{cov}}\newcommand{\d}{\mathrm{d}}\cov(x,y) = \iint (F_{X,Y}(x,y) - F_X(x)F_Y(y))\,\d x\,\d y$$ However, I have no idea how to start. I know that $... 0answers 24 views ### Expected function evaluation of random variable w.r.t. different distribution Suppose I have two continuous random variables on the same domain,$\xi \sim \mathbb{P}, \xi' \sim \mathbb{Q}, \in \Xi$and joint probability$(\xi, \xi') \sim \Pi \in \Xi^2. Now I would like to ... 0answers 28 views ### How to evaluate double Integral with importance sampling I am trying to recreate the Bayesian Hierarchical Clustering algorithm using Python. The example in section two requires evaluating the following double integral (univariate case): \begin{align} p(... 0answers 18 views ### The joint distribution of Y=AX and Z=BX given a projection matrix A and residual maker matrix B, and a random vector X with known pdf? This question follows on from a previous question I asked which was answered. It turns out my question lacked some important details, which was revealed by the answer posted on that thread. This is ... 0answers 11 views ### create joint prob distribution or empirical relation for two variables There are two variables, X1 and X2. The experimental study shows that they are highly correlated. Are there any reliable ways to create an empirical mapping(or equation) between X1 and X2. Assuming ... 0answers 14 views ### identifying which ofd$normal distribution generated a given sample I have$d$Normal Distributions,$N_1(\mu_1, \sigma_1^2) \cdots N_d(\mu_d, \sigma_d^2)$. We pick one of the$d$distributions with each distribution having a probability of$\frac{1}{d}$of being ... 0answers 10 views ### Line of Best Fit If we have a dataset with two variables, X & Y, we can find the line of best fit using the empirical data (and whatever method suits you best). However, what if know the true joint distribution ... 0answers 51 views ### Combining subjoint distributions to create a larger joint distribution I am trying to construct large joint distributions through smaller joint distributions and I'm not sure how to approach the literature. I am curious if there exists a function which can take n ... 0answers 30 views ### Optimize an objective based on a trained model I want to find a joint optimal subset based on individual scores from a predictive model. Example: Say I have a set of customers and a set of products. And I have trained a model for predicting the ... 0answers 14 views ### Probability of successful match with two faces in image A photo containing faces of two different people is compared to labeled images of faces in database. The probability of a match on the first person is .70. The probability of a match on the second ... 0answers 35 views ### Joint Probability Distribution and covariance If $$f(x,y)=1/4$$$x=-3,y=-5; x=-1,y=-1; x=1,y=1; x=3,y=5. $Find cov (x,y). I know the formula for cov (X,Y) but I'm stuck at finding E (x) and E (y). 0answers 42 views ### Resample from data with constraints to the marginal distribution Motivation This problem comes from the situation where I have a non-random sample of individuals for which$p$variables are measured. The target is to extract a subset of individuals which would be ... 0answers 34 views ### How is exchangeability related to covariate shift? I understand that exchangeability refers to the notion that the order of data in a sequence does not affect the joint distribution of that data. In a sense, the current data we possess is from the ... 0answers 75 views ### Joint probability distribution of geometric distribution Let$X$and$Y$be independent and identically distributed$(i.i.d.)$r.v.’s, each having the probability distribution,$p(k) = (1 − λ)λ^k$;$k = 0,1,...$where$λ :(0; 1)$is a constant. Define$U = ...
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 ...