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Unifrom distribution of a disc

  1. Oct 28, 2009 #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
    0 \mbox{otherwise}[/tex]
    as the area of the disc [tex]\pi[\tex] and to make it uniform you divide by [tex]\pi[\tex] so the probability integrates to 1

    i apologise in advance for posting the same thing twice. i dont know how to delete 1 of them
     
    Last edited: Oct 28, 2009
  2. jcsd
  3. Oct 29, 2009 #2

    lanedance

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    Homework Helper

    how do you get that probabilty density function? as the dsitribution is uniform, i think the probabilty of finding x&y in any region should be proportional to its area

    also in line you can use itex rather than tex, [itex] f_{xy} = [/itex] and functions within use the \ back-slash whilst to close the tex use the / forward slash
     
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