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Math Help - Uniform Distribution of a Circle

  1. #1
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    Uniform Distribution of a Circle

    Suppose that (X_i, Y_i), i = 1,...,n is a 2D sample, with each (X_i, Y_i) assumed to be uniformly distributed in a circle centered at the origin of an unknown radius r.

    How do I calculate the pdf of this?

    I'm thinking \frac{1}{\pi r^2} but I don't think this is correct.
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  2. #2
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    Quote Originally Posted by BERRY View Post
    Suppose that (X_i, Y_i), i = 1,...,n is a 2D sample, with each (X_i, Y_i) assumed to be uniformly distributed in a circle centered at the origin of an unknown radius r.

    How do I calculate the pdf of this?

    I'm thinking \frac{1}{\pi r^2} but I don't think this is correct.
    The uniform distribution in the disc of radius r has indeed the following p.d.f.: \frac{1_{(x^2+y^2\leq r^2)}}{\pi r^2}.

    (sometimes it is more useful to have an expression in terms of polar coordinates)
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