# 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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Let $\Omega$ be a sample space and $\mathbb{Q}=(\Omega, \mathcal{F}, \mathbb{P})$ standard probability space. Suppose that there exeist three different functions, say $$\mu:\Omega\to\Delta(X)$$ $$\tau:... 1 vote 1 answer 64 views ### Question regarding conditional and marginal distributions I’ve stumbled upon this figure. You can see that the shaded area represents the conditional density function:$$f_{X_1|X_2}(x_1|x_2) = \frac{f(x_1,x_2)}{f_{X_2}(x_2)}$$At the same time, this shaded ... 0 votes 0 answers 28 views ### Marginal Distribution Rewriting Equation I have a question, for which I could not find an answer on the Internet. Given the formula for the marginal distribution:$$ p(x|c) = \int p(x|z,c)p(z|c)dz $$Is it allowed to rewrite this equation to ... 3 votes 1 answer 144 views ### Finding the probability of a point bounded in a region from its joint pdf Let R be the region in \mathbb{R}^2 bounded by the three lines y=2.1, y=x, y=−x and contains the point (0,\frac{1}{2}). Let (X,Y) be the coordinate of a point chosen uniformly at random ... 1 vote 0 answers 64 views ### Same marginals and covariance but different joint distribution? The question and answer in: If marginal probabilities equal, can we say anything about joint distribution? gives an example such that one can have two different joint distribution from the same ... 0 votes 0 answers 9 views ### Approximating the marginal of nested Wishart distributions Consider that you have the following joint distribution over two matrices A and B both of which are of size p \times p:$$ B \sim \mathcal{W}_p(S, n) \quad \quad A|B \sim \mathcal{W}_p(B, n)$$... 0 votes 1 answer 118 views ### Calculate marginal pdf of Y when marginal pdf of X and conditional distribution of Y is given The Question So I have tried the formula f_{X,Y}(x,y)=f_{Y\mid X}(y\mid x)\cdot f_{X}(x) but I am not able to figure out the bounds and I am not sure what to do after the bounds are found Please do ... 1 vote 0 answers 45 views ### analytic multivariate Lorenz surfaces I am given the projections of a multivariate probability distribution and asked to recover the multivariate distribution. How do I derive the copula? How do I use the copula to define the joint ... 1 vote 1 answer 62 views ### How to show the Joint CDF I have a such example in my text book Let Y and Z be two IID random variables each with CDF, F(\cdot). Let X_1:=min(Y,Z) and X_2:=max(Y,Z) with marginals F_1(\cdot) and F_2(\cdot), ... 0 votes 1 answer 37 views ### Mixture models vs marginal distributions Maybe I'm not understanding these concepts correctly, but it seems like the idea of a mixture model seems to be superfluous, since we can express any mixture of random variables as a multivariate ... 1 vote 0 answers 18 views ### Marginalization of intermediate variables p(w|z, y) = \int_z p(w| x, z)p(z| x, y)dz I want to know if my statement and derivation of the marginalization of the "intermediate" variable is correct. The statement is as follows: Suppose a probabilistic factorization model p(x,... 0 votes 1 answer 33 views ### Obtain P(A,B,C) from P(A,B) and P(B,C) if A and C are independent If I am given the data of the marginals P(A,B) and P(B,C) together with the promise that A and C are independent, i.e. P(A,C)=P(A)P(C), then, is there a way to deduce the full distribution ... -1 votes 1 answer 30 views ### Is this question correct because if I find the PDF in terms of X and Y wouldn't that be the marginal PDF f XY(x,y)? [closed] Let S = { (𝑥,𝑦,𝑧) ∈ R³ | (𝑥² + 𝑦² + 𝑧²) ≤ 1, 𝑧 ≥ 0 } for any lebesgue measurable subset A of S, let P(A) = (3÷(2π)) × (volume of A) let X (𝑥,𝑦,𝑧) = 𝑥 and Y(𝑥,𝑦,𝑧) = 𝑦, ∀(𝑥,𝑦,𝑧) ∈ S. ... 0 votes 0 answers 56 views ### Computing Tables of Random Vectors I have been trying to solve problems on random vectors, given their joint pmf table computing their expectation, variance and filling in the joint probability. I am finding difficult the filing joint ... 0 votes 1 answer 53 views ### Understanding this derivation of a conditional distribution for an autoregressive process In a current paper I am reading, the following section shows up as a side note. I am not sure I understand the derivation the authors propose here: Consider the following auto-regressive process:$$...
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)...
### 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 $f_X,_Y(x,k)$ ...