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Help understanding a set and its distribution

  1. Nov 2, 2015 #1
    1. The problem statement, all variables and given/known data
    given set C = {(x,y)|x,y are integers, x^2 + |y| <= 2}

    Suppose they are uniformly distributed and we pick a point completely at random, thus p(x,y)= 1/11

    2. Relevant equations
    Listing it all out,
    R(X) = {-1,-2,0,1,2} = R(y)

    3. The attempt at a solution
    My problem is that when I list those out, I get a probability of 1/13, not 1/11...
    (0,0)
    (0,1)
    (0,-1)
    0,-2)
    (0,2)
    (1,0)
    (-1,0)
    (1,1)
    (1,-1)
    (-1,1)
    (-1,-1)
    (2,0)
    (-2,0)

    Maybe it's late and I'm making a mistake
     
    Last edited by a moderator: Nov 2, 2015
  2. jcsd
  3. Nov 2, 2015 #2
    (2,0) and (-2,0) do not satisfy the inequality
     
  4. Nov 2, 2015 #3
    There it is, wow. Thank you. I was clearly tired
     
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