What is the Probability Density Function for a Uniform Distribution on a Disc?

[rosh300]

Homework Statement

$$\D = \{(x,y) \in \mathbb{R}^2 | x^2 + y^2 \leq 1\}$$ i.e. a disc or radius 1.
Write down the pdf f_{xy} for a uniform distribution on the disc.

Homework Equations

The Attempt at a Solution

$$f_{xy} = \frac{(x^2 + y^2)}{\pi} \mbox{for} x^2 + y^2<br /> 0 \mbox{otherwise}$$
as the area of the disc [tex]\pi[\tex] and to make it uniform you divide by $$\pi[\tex] so the probability integrates to 1<br /> <br /> i apologise in advance for posting the same thing twice. i don't know how to delete 1 of them$$[/tex]

 

[lanedance]

how do you get that probability density function? as the dsitribution is uniform, i think the probability of finding x&y in any region should be proportional to its area

also in line you can use itex rather than tex, $f_{xy} =$ and functions within use the \ back-slash whilst to close the tex use the / forward slash