Questions tagged [marginal-distribution]

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67 questions
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I need to find the marginal distribution of Y from the following distributions

$f_X(x) = \frac{1}{2}e^{\frac{-x}{2}}$ and $f_{Y|X}(y|x) = I_{[0;x^2]}$ (Uniform continuous from $0$ to $x^2$). I tried finding the joint distribution by using $f(X,Y) = f(Y|X) * f(X)$ and then ...
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I'm trying to find a marginal distribution for a function and I need to solve the integral bellow.

I have arrived at the following integral: $$\int_y^\infty \frac{e^{-x/2}}{2x^2}$$ The limits I'm not so certain, but the function is correct. I have tried integration by parts but I arrived at a more ...
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What is better way to estimate marginal density?

Let there be the random variables $X$ and $Y$. We have a sample of $X$'s and Y's together. To most accurately estimate the density $f_X$, would we... 1) Ignore the Y's and estimate $f_X$ only from ...
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Is there any connection between marginal distributions and derivatives?

I know that "marginal" in "marginal distribution" is due to the fact that the marginal distributions of the discrete variables $X$ and $Y$ appear on the margin of the table used to express the ...
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Marginal distribiution of X and Y

"The joint density function of (X,Y) is given by: f(x,y)=2 for |x|<=0.5,|y|<=0.5 and xy>=0.Otherwise f(x,y) equals 0. Find the marginal distribitions of X and Y and check if they are independent....
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Joint PDF from Copula

I have two 1-d distributions and the correlation between them. I want to add them together, but to do this I'll need their joint distribution. I stumbled across copulas which seemed like a promising ...
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Find the density function of a random variable that depends on two other random variables with a given joint distribution.

For example, The joint density of $X$ and $Y$ is given by $$f(x, y) = \begin{cases}e^{-x-y}&\text{ if } 0<x<\infty, 0<y<\infty\\ 0 &\text{ otherwise}\end{cases}.$$ Find the ...
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Find joint CDF given a joint PDF

Let $X$ and $Y$ have a joint density function given by $$f(x, y) = \begin{cases} 1, & \text{for } 0\leq x\leq2,\;\max(0,\,x-1)\leq y\leq \min(1,\,x), \\ 0, & \text{otherwise}. \end{cases}$$...
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Marginal distribution of sum of Poisson random variables from i=2 to n

This is a simple question but I'm not sure what to do when we're not summing the distributions from $i=1$ to $i=n$. Let's assume $X_1, \dots, X_n$ are i.i.d observations sampled from a Poisson ...
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Bayesian Statistics: Marginal Posterior

In a hierarchical model, the prior $\pi(\theta\mid\xi)$ for $\theta$ depends on hyperparameters $\xi$. In my lecture notes, the following is now given:  \pi(\xi \mid x) = { \pi(\theta,\xi\mid x)\...