Finding Marginal Pdf's for a Joint PDF

In summary, we have a random vector (X, Y) with a probability density function of fX,Y (x, y) = k(x-y), if 0<y<x<1 and 0 otherwise. To make this a genuine pdf, we must have k = -6. To find the marginal density functions of X and Y, we can reverse the order of integration and find fX(x) = 3x^2 and fY(y) is still unknown.
  • #1
hoddo
5
0
Joint PDF --> Marginal Pdf's

Homework Statement



Suppose that the random vector (X, Y ) has the probability density function
(pdf)
fX,Y (x, y) = k(x − y), if 0 < y < x < 1
0, otherwise.
1. Find the value of k, so that fX,Y (x, y) is a genuine pdf.
2. Find the marginal density function of Y , fY (y) and of X, fX(x).


Homework Equations





The Attempt at a Solution


1. k = -6 (using 0<y<x, 0<x<1)
2. fY(y) ?
fX(x) = 3x^2

...having trouble finding fY(y) that eventuates at a true pdf?
 
Physics news on Phys.org
  • #2
hoddo said:
k = -6
How can it be negative? That would make f(x,y) negative.
hoddo said:
having trouble finding fY(y)
Just reverse the order of integration.
 

FAQ: Finding Marginal Pdf's for a Joint PDF

1. What is a Joint PDF?

A Joint Probability Density Function (Joint PDF) is a mathematical function that describes the probability of multiple continuous random variables taking on specific values at the same time.

2. How is a Joint PDF related to Marginal PDFs?

Marginal PDFs are derived from a Joint PDF by integrating out one or more of the variables. This allows us to study the probability distribution of individual variables separately, while still considering their relationship to the other variables.

3. What information can we get from Marginal PDFs?

Marginal PDFs can provide information such as the range of values a variable can take, the likelihood of a variable taking on a specific value, and the average value of a variable.

4. Can we calculate Marginal PDFs from a Joint PDF?

Yes, Marginal PDFs can be calculated by integrating the Joint PDF over the variables that are not of interest. This process is known as marginalization.

5. Why are Marginal PDFs useful in probability and statistics?

Marginal PDFs allow us to study the behavior of individual variables in a multivariate system, while still considering their relationship to other variables. This makes them extremely useful in modeling and analyzing complex systems, such as in finance, economics, and engineering.

Similar threads

Probability problem -- The joint PDF of X and Y is uniform on this rectangle....
Replies
11
Views
2K
Determine marginal densities and distributions from joint density
Replies
7
Views
777
Marginal pdf, what am I doing wrong?
Replies
5
Views
2K
Marginal Probability Distribution
Replies
3
Views
2K
Finding marginal distribution of 2d of probability density function
Replies
6
Views
1K
Determine marginal distribution of random vector on unit sphere
Replies
9
Views
1K
Joint probability distribution
Replies
2
Views
1K
Distribution of a Function of a Random Variable
Replies
7
Views
2K
Find marginal pdf given joint pdf (stats)
Replies
3
Views
2K
What is the Marginal PDF of X?
Replies
4
Views
3K

Hot Threads

Recent Insights

Back
Top