All Questions
12 questions
3
votes
1
answer
177
views
Calculate expected values E(x) & E(y) & variance of x & y of joint PDF, which was previously transformed from Polar to Cartesian
Given two independently uniform distributed random variables angle $\theta \in [0,2\pi]$ and radius $r \in [0,1]$.
I obtain for the joint density function with polar coordinates: $$ f_{r,\theta}(r,\...
- 33
4
votes
2
answers
373
views
What is the copula of a variable with itself?
In Sklar's theorem for joint probability functions,
$$f(x,y) = c(F_X(x), F_Y(y)) \cdot f(x) f(y)$$
the copula is $c(\cdot)$ of variables $X$ and $Y$, while $f(\cdot)$ are their marginal distributions.
...
- 4,049
1
vote
1
answer
46
views
Marginal distribution
A loss distribution has PDF - $f(x) = 1/x^2$, for $x > 1$
An insurer finds that the time in hours it takes to process a loss amount x has a uniform distribution on the interval $(\sqrt x, 2\sqrt x)$...
3
votes
1
answer
102
views
Finding P(a< u(X,Y) <b) given a rectangular support
>The continuous variables X and Y have the following joint pdf $f(x,y) = x + y, 0<x,y<1.$
Determine $P(0.5<X+Y<1.5)$.
I know that the support of x and y is rectangular, hence they are ...
- 33
1
vote
1
answer
498
views
Computing a marginal distribution of a joint involving a delta function
Suppose that we have four continuous random variables $x,y,z,$ and $v$ and we want to compute the following integral:
$$\int f(x\mid y)f(z\mid x,y)f(v\mid z,x,y)\,dx$$
There are a few conditions:
$...
- 286
0
votes
1
answer
38
views
Setting boundaries for calculating $P(Y/X>2)$ choosing $dx/dy$ order [duplicate]
Given two independent variables $X$ and $Y$, with marginal pdfs $f_X(x)=2x,
0 \le x \le 1$ and $f_Y(y)=1, 0 \le y \le 1$, calculate $P(\frac{Y}{X} > 2)$. So this can be written as $P(Y>2X)$,
...
- 115
3
votes
1
answer
9k
views
Finding the joint CDF using the joint PDF; why can't I do this?
Find the joint CDF of the independent random variables $X$ and $Y$, where
$f_X(x)=x/2, 0\le x \le 2, $ and
$f_Y(y)=2y, 0 \le y \le 1$.
To do this, we can find the CDF separately for each of the ...
- 115
4
votes
2
answers
360
views
Having difficulty deciding limits of integration for a joint to marginal pdf
A joint pdf, $f_{X,Y}(x,y)=5$, is given with the following intervals:
$-1<x<1$
$x^2<y<x^2+{1\over{10}}$
I am trying to find the marginal pdf of $f_Y(y)$ but I am stuck.
2
votes
1
answer
283
views
Is it possible to obtain joint PDF of set of variables given marginal PDF of each variable?
Say $f(X_1)$, $f(X_2)$, $f(X_3)$, $f(X_4)$ are the empirical marginal PDFs of random variables $X_1$, $X_2$ , $X_3$, $X_4$. Also given is correlation between each pair of variables $X_1$, $X_2$ , $X_3$...
- 422
4
votes
2
answers
1k
views
Interpretation of cartesian product of the support of marginal distribution
Suppose we have a multivariate data set, $s = (s_1, s_2, ... s_p)$ and each $s_i$ is distributed with a distribution that has finite support (we'll call each $s_i$ a "source"). Let us ...
- 872
1
vote
0
answers
926
views
Marginal distribution of a function of order statistics
From the joint distribution of any two order statistics, say $Y_j$ and $Y_k$, $j<k$ I would like to derive the distribution of $Z=F(Y_k)-F(Y_j)$.
The initial pdf is:
$$f_{Y_j,Y_k} (y_j,y_k) =\...
- 21.1k
10
votes
2
answers
11k
views
Problem calculating joint and marginal distribution of two uniform distributions
Suppose we have random variable $X_1$ distributed as $U[0,1]$ and $X_2$ distributed as $U[0,X_1]$, where $U[a,b]$ means uniform distribution in interval $[a,b]$.
I was able to compute joint pdf of $(...
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