# 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.

237 questions
Filter by
Sorted by
Tagged with
19 views

### Different approaches to finding the marginal distribution on surface of sphere with radius $R$ centered at origin.

I asked this question years ago $f_X(x) \neq \frac{2 \pi \sqrt{R^2 - x^2}}{4\pi R^2}$? $X$ belongs to points uniformly distributed on the surface of a sphere., and I'm trying to use 2 other ...
21 views

### Finding Marginal Distribution of a multivariate function

Suppose I have a function $$f(x,y,z) \propto x^2yz(1-2x-y-z)$$ where $x>0,y>0, z>0, 2x+y+z<1$ I need to find the marginal functions of X, Y and Z. In normal, two-variable situations, I ...
25 views

21 views

### Proving Lemmas in Gaussian Distribution

I am struggling to prove the following lemmas: How would you suggest me to solve it?
1 vote
40 views

### If $X\sim G(a,b_{1})$ and $Y\sim G(a,b_{2})$, then what will be the density function for U=min(X,X+Y)?

Let $X$ and $Y$ two independent random variables for gamma distributions with common shape parameter $a$ and different rate parameter $b_{1}$ and $b_{2}.$ If $U=\min(X,X+Y),$ then what will be the ...
34 views

### Understanding change of probability density function or proability mass function when "Marginal probability distribution" rule

Nobody actually tell me this simple question so I ask here. For below formula, probability distribution marginalizing, does P(X) and P(X, Y) share same form of PDF or PMF? I assume the PDF or PMF will ...
189 views

### Marginal density equal to zero everywhere.

I've been working on a two part question on bivariate transformations and marginal densities but am having difficulty finding where I have made a mistake as the final answer for the marginal density ...
90 views

### Joint laws and marginal laws

We have 10 marbles enumerated from 1 to 10, and two boxes $B_1,B_2$. Marbles are inserted randomly in boxes. Let $X$ be a random variable counting the number of marble in $B_1$ and $Y$ a random ...
201 views

### Using general bivariate gaussian to extract marginal PDF from given bivariate PDF

I had a homework question to find the marginal probability density functions, $p_X(x)$ and $p_Y(y)$, given a join probability density function $p_{XY}(x,y)$. I have solved the problem by integration i....