How to Find the PDF 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 \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

 

[gabbagabbahey]

Hmmm...

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

Doesn't look very uniform to me

 

[rosh300]

i think i got it: its <br /> f(x,y)_{xy} = \left\{ \begin{array}{rl}<br /> \frac{1}{\pi} &amp;\mbox{for } x^2 + y^2 \leq 1\\<br /> 0 &amp;\mbox{otherwise}<br />

thanks

 

[gabbagabbahey]

Looks good to me!

 

[lordslytherin]

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