# unifrom distribution of a disc

by rosh300
Tags: disc, distribution, probability density, statistics
 P: 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
 HW Helper P: 5,004 Hmmm... $$f_{xy} = \frac{(x^2 + y^2)}{\pi}$$ Doesn't look very uniform to me
 P: 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
HW Helper
P: 5,004

## unifrom distribution of a disc

Looks good to me!
 P: 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

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