A circular target has radius 1 foot. Assume that you hit the target (we shall ignore misses)

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A circular target has radius 1 foot. Assume that you hit the target (we shall ignore misses) and that the probability of hitting any region of the target is proportional to the region’s area. If you hit the target at a distance Y from the center, then let X = πYbe the corresponding area. Show that

a. X is uniformly distributed on [0, π].

b. Y has pdf ƒY(y) = 2y, 0 < y < 1.

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Modern Mathematical Statistics With Applications

ISBN: 9783030551551

3rd Edition

Authors: Jay L. Devore, Kenneth N. Berk, Matthew A. Carlton

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