# Questions tagged [marginal-distribution]

Marginal probability distributions arise from joint probability measures on product spaces. The marginal distributions are the push-forward measures induced by the coordinate projections.

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### Marginalize Gaussian from exponential family distribution

Consider the marginal distribution $$p(y|z)=\int p(y|f)p(f|z)df$$ where $p(y|f)$ a generic distribution in the exponential family and $p(f|z)$ is Gaussian and the parameters of both distributions ...
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### Posets for conditional distributions over n variables

When considering distributions of up to n variables, enumerating the set of all joint and marginal distributions forms a poset conveniently arranged in an n-cube: poset of 0 to 3 variables. Thus there ...
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### Marginal probability of Y at a point

A car vendor sells type A and type B cars. Consider that X and Y represent the types A and B of cars being sold (respectively). Consider the Random Pair (X, Y) to have probability function according ...
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### Defining joint distribution of two uniform variables where one is bounded by the other

I want to know how to define the joint distribution between two continuous uniform random variables. The first variable, X, is simply X ~ U(0, 1). The second variable, Y, can also vary between 0 and 1,...
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### Mean of n-dimensional uniform unit-ball

Suppose I have an $n$-dimensional unit-ball: $$\{(t_1,...,t_n) : t_1^2+...+t_n^2\le1\}$$ And suppose I have an $n$-dimensional random variable $(X_1,...,X_n)$ who distributes uniform in this unit-...
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### Find the marginal densities of $X$ and $Y$ knowing $h(x,y)$

I have the distribution with joint density $h$ (with respect to the Lebesgue measure): $$h(x,y)=\frac{3}{2}y 1_{A}(x,y), \ \ A=\{(x,y) \in R^2|0<y, x^2+y^2<1\}$$ And then I have to find the ...
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### Does weak convergence of measures preserve independence of marginals?

Let $X^n = (X^n_1, \dots, X^n_d) ~ q^n$ be a $d$-dimensional random variable, where all the components are independent. That is, $X_i \perp X_j$ for $i\neq j$, and q^n(X) = \prod_{i=1}^d q^n_i(X^n_i)...
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### For given Joint pdf, Find the value of $c$
My Working: So I have been practicing for my upcoming exam. This is from one of my past exam papers, and I am unable to solve it. The thing that confuses me is that the given pdf $f_X,_Y(x,k)$ ...