# 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 expectation of two identical marginal normal random variables

Let $Y_0$ and $Y_1$ be both identically (not necessarily independent) normally distributed with mean $\mu$ and $\sigma^2$, i.e., $Y_i \sim N(\mu, \sigma^2)$ for $i = 1, 2$. Let $\rho$ denote the ...
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### Same Joint Distribution, different conditional and marginal distribution

I have a group of samples drawn from density function $p(x,y)$, so it has the marginal density $p(x)$ and $p(y)$, and conditional density $p(x|y)$ and $p(y|x)$. In what way I can construct another ...
2answers
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### If any two variables follow a normal bivariate distribution does it also have a multivariate normal distribution?

Bivariate and multivariate distribution relationship. If we have say 3 variables where any two variables follow a normal bivariate distribution, then does it necessarily follow a multivariate ...
1answer
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### Obtain marginal CDF from joint CDF by simulation

How can I evaluate the marginal cumulative distribution function of a set of random variables for which I do not have the CDF in closed form. I can, however, simulate from a joint distribution ...
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### How can one construct a cumulative probability distribution function from 2 others?

I dip into project time estimation and can't find intuition. What is the cumulative probability distribution of an event when two independent tasks both complete successfully (when performed in ...
1answer
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### Generating samples from Copula in R

Suppose I want to model dependence between $d$ r.v.´s $Y_1,...,Y_d$ with the copula $C_\theta$, where $\theta$ are the corresponding parameters of that copula. I've also determined the correlation ...
1answer
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### Relations between probabilities of “almost” independent random variables

Let $X$ and $Y$ be two random variables, such that the (average) mutual information is very small: $$0 \le I(X;Y) \le \epsilon \ll 1$$ In this case, we say that $X$ and $Y$ are almost independent. ...
0answers
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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 $Z_1$ ...
2answers
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### Is it possible to derive joint probabilities from marginals with assumptions about the conditionals?

I understand the title is too generic. I tried to look for similar questions and although there were a few that were seemingly about the same issue, either they provided answers in the negative or had ...
1answer
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