Suppose that a particle is released at the origin of the xy-plane and travels into the half-plane

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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 α, which can be either positive or negative. Suppose, finally, that the angle α has the uniform distribution on the interval [−π/2, π/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.
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...
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Probability And Statistics

ISBN: 9780321500465

4th Edition

Authors: Morris H. DeGroot, Mark J. Schervish

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