Unifrom distribution of a disc

1. rosh300

17
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

2. gabbagabbahey

5,008
Hmmm...

$$f_{xy} = \frac{(x^2 + y^2)}{\pi}$$

Doesn't look very uniform to me

3. rosh300

17
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

Last edited: Oct 28, 2009
4. gabbagabbahey

5,008
Looks good to me!

5. lordslytherin

5
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