Unifrom distribution of a disc

  1. 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. jcsd
  3. gabbagabbahey

    gabbagabbahey 5,013
    Homework Helper
    Gold Member

    Hmmm...

    [tex] f_{xy} = \frac{(x^2 + y^2)}{\pi}[/tex]

    Doesn't look very uniform to me:wink:
     
  4. 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
     
    Last edited: Oct 28, 2009
  5. gabbagabbahey

    gabbagabbahey 5,013
    Homework Helper
    Gold Member

    Looks good to me!:approve:
     
  6. 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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