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 = πY2 be 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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Related Book For
Modern Mathematical Statistics With Applications
ISBN: 9783030551551
3rd Edition
Authors: Jay L. Devore, Kenneth N. Berk, Matthew A. Carlton
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