## unifrom distribution of a disc

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

$$f_{xy} = \frac{(x^2 + y^2)}{\pi} \mbox{for} x^2 + y^2 \leq 1$$ 0 otherwise
as the area of the disc pi and to make it uniform you divide by pi so the probability integrates to 1
 PhysOrg.com science news on PhysOrg.com >> King Richard III found in 'untidy lozenge-shaped grave'>> Google Drive sports new view and scan enhancements>> Researcher admits mistakes in stem cell study
 Recognitions: Homework Help Hmmm... $$f_{xy} = \frac{(x^2 + y^2)}{\pi}$$ Doesn't look very uniform to me
 i think i got it: its $$f(x,y)_{xy} = \left\{ \begin{array}{rl} \frac{1}{\pi} &\mbox{for } x^2 + y^2 \leq 1\\ 0 &\mbox{otherwise}$$ thanks

Recognitions:
Homework Help

## unifrom distribution of a disc

Looks good to me!
 I am doing a some practice questions for stats and i tried to integrate this to get 1 but i can't so what are the appropriate limits and how would i go about finding the marginal distribution of x and y? Thanks

 Tags disc, distribution, probability density, statistics