Stat 231 Exam 1 S10 Sol

Stat 231 Exam 1 S10 Sol - Stat 231 Exam 1 Spring 2010 I...

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1 Stat 231 Exam 1 Spring 2010 I have neither given nor received unauthorized assistance on this exam. ________________________________________________________ Name Signed Date _________________________________________________________ Name Printed
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2 1. A not-so-excellent marksman fires at a solid-circular target of radius 1 ft, and shots hitting the target might be modeled as uniformly distributed inside the circle. If one thinks of the center of the target as the origin of coordinate axes, and , XY as the coordinates of the random location of a hit on the target, a sensible joint pdf for and is 22 1 if 1 , 0 otherwise xy fxy and this is pictured to the right. a) For 0 1 r , what is the probability that a shot hitting the target lands within r feet of the center? (This is PXY r .) b) Find the marginal probability density for X , gx . (Be sure to say completely where any expression you propose for applies.) c) Find the conditional probability density for Y given that 1 2 X . (Again be very careful to say completely where any expression you propose for 1 | 2 hy applies.) 7 pts 7 pts 7 pts
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3 2. A lathe turns out cylinders with diameters that are normally distributed with mean 3.02 cm and
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This note was uploaded on 02/11/2012 for the course STAT 231 taught by Professor Staff during the Fall '08 term at Iowa State.

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Stat 231 Exam 1 S10 Sol - Stat 231 Exam 1 Spring 2010 I...

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