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Suppose that a particle is released at the origin of the

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Suppose that a particle is released at the origin of the xy-plane and travels into the half-plane where x > 0. Suppose t

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Suppose that a particle is released at the origin of the xy-plane and travels into the half-plane where x > 0. Suppose that the particle travels in a straight line and that the angle between the positive half of the x-axis and this line is ?, which can be either positive or negative. Suppose, finally, that the angle ? has the uniform distribution on the interval [??/2, ?/2]. Let Y be the ordinate of the point at which the particle hits the vertical line x = 1. Show that the distribution of Y is a Cauchy distribution.

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