# Unifrom distribution of a disc

1. Oct 28, 2009

### rosh300

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. The attempt at a solution

$$f_{xy} = \frac{(x^2 + y^2)}{\pi} \mbox{for} x^2 + y^2 0 \mbox{otherwise}$$
as the area of the disc [tex]\pi[\tex] and to make it uniform you divide by [tex]\pi[\tex] so the probability integrates to 1

i apologise in advance for posting the same thing twice. i dont know how to delete 1 of them

Last edited: Oct 28, 2009
2. Oct 29, 2009

### lanedance

how do you get that probabilty density function? as the dsitribution is uniform, i think the probabilty 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