1. The problem statement, all variables and given/known data [tex]\D = \{(x,y) \in \mathbb{R}^2 | x^2 + y^2 \leq 1\} [/tex] 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 [tex] f_{xy} = \frac{(x^2 + y^2)}{\pi} \mbox{for} x^2 + y^2 \leq 1[/tex] 0 otherwise as the area of the disc pi and to make it uniform you divide by pi so the probability integrates to 1
i think i got it: its [tex] f(x,y)_{xy} = \left\{ \begin{array}{rl} \frac{1}{\pi} &\mbox{for } x^2 + y^2 \leq 1\\ 0 &\mbox{otherwise} [/tex] thanks
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