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    Acceptance-rejection sampling on unit disc

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    Suppose that the random variables X and Y are independent and uniform on the interval [-1, 1]. You form a random variable Z by sampling from X and Y and computing X^2 + Y^2. Whenever X^2 + Y^2 > 1 the sample is rejected, otherwise it is accepted. Prove that Z is uniformly distributed on [0, 1].

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    Question:
    Suppose that the random variables X and Y are independent and uniform on the interval [-1, 1]. You form a random variable Z by sampling from X and Y and computing X^2 + Y^2. Whenever X^2 + Y^2 > 1 the sample is rejected, otherwise it is accepted. Prove that Z is uniformly distributed on ...

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