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Unifrom distribution of a disc 
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#1
Oct2809, 01:13 PM

P: 17

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 


#2
Oct2809, 02:25 PM

HW Helper
P: 5,003

Hmmm...
[tex] f_{xy} = \frac{(x^2 + y^2)}{\pi}[/tex] Doesn't look very uniform to me 


#3
Oct2809, 03:17 PM

P: 17

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 


#5
Oct2610, 03:20 PM

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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