Uniform distribution on the disc

In summary, the conversation discusses a homework question about a disc of radius 1 in the plane D in R^2 and the marginal pdf of x and y. The joint distribution of xy is 1/Pi for x^2 + y^2 <=1, with the density being equal to the probability divided by the area. The area is Pi, but it is unclear why the probability is 1. The question of the marginal pdf of x and y is also brought up and the possibility of it being the integral of 1/Pi from -infinity to +infinity with respect to y is mentioned. There is also a mention of the conversation being posted in two locations by mistake.
  • #1
mathmathmad
50
0

Homework Statement



consider a disc of radius 1 in the plane D in R^2
D = {(x,y) in R^2 | x^2 + y^2 <=1 }
what is the marginal pdf of x and y

Homework Equations





The Attempt at a Solution


so the joint distribution of xy is 1/Pi for x^2 + y^2 <=1 right?
but how exactly? "density" = "probability" / "area"
area = Pi since Pi*(1)^2 what about the probability? why is it 1?

what is the marginal pdf of x and y?
is it integral of 1/Pi from -infinity to +infinity wrt to y for marginal pdf of x?
 
Physics news on Phys.org
  • #2
why did you post this in two locations? look at your other post.
 
  • #3

1. What is a uniform distribution on the disc?

A uniform distribution on the disc is a probability distribution where all points within a disc have an equal chance of being selected. This means that the probability of selecting any point within the disc is the same.

2. How is a uniform distribution on the disc different from a uniform distribution on a line?

A uniform distribution on a line has an equal probability of selecting any point along the line, while a uniform distribution on the disc has an equal probability of selecting any point within the disc's area.

3. What is the formula for calculating the probability density function of a uniform distribution on the disc?

The formula for the probability density function of a uniform distribution on the disc is f(x,y) = 1/πr2, where r is the radius of the disc and x and y are the coordinates of the point within the disc.

4. How is a uniform distribution on the disc used in statistics?

In statistics, a uniform distribution on the disc can be used to model situations where there is no preference or bias towards any particular point within the disc. It is also used in simulations and random sampling methods.

5. What are some real-life examples of a uniform distribution on the disc?

Examples of a uniform distribution on the disc can be seen in scenarios such as the distribution of particles within a circular container, the distribution of rainfall within a circular region, and the distribution of points on a dartboard.

Similar threads

Finding marginal distribution of 2d of probability density function
    • Calculus and Beyond Homework Help
Replies
6
Views
1K
Variance of a point chosen at random on the circumference of a circle
    • Calculus and Beyond Homework Help
Replies
9
Views
2K
Calculating Volume of a Sphere Using Integration: What Mistakes Have I Made?
    • Calculus and Beyond Homework Help
Replies
14
Views
1K
Center of mass of spherical shell inside of cone (Apostol Problem).
    • Calculus and Beyond Homework Help
Replies
3
Views
562
Computing line integral using Stokes' theorem
    • Calculus and Beyond Homework Help
Replies
8
Views
876
Integration problem using inscribed rectangles
    • Calculus and Beyond Homework Help
Replies
14
Views
247
Calculate this Integral around the Circular Path using Green's Theorem
    • Calculus and Beyond Homework Help
Replies
3
Views
276
Flux through top part of sphere
    • Calculus and Beyond Homework Help
Replies
6
Views
959
Change of variables in multiple integrals
    • Calculus and Beyond Homework Help
Replies
34
Views
2K
Probability problem -- The joint PDF of X and Y is uniform on this rectangle....
    • Calculus and Beyond Homework Help
Replies
11
Views
1K

Hot Threads

Recent Insights

Back
Top