Stat 231 Exam 1 S10

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

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Stat 231 Exam 1 Spring 2010 I have neither given nor received unauthorized assistance on this exam. ________________________________________________________ Name Signed Date _________________________________________________________ Name Printed
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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 ( ) , X Y as the coordinates of the random location of a hit on the target, a sensible joint pdf for and X Y is () 22 1 if 1 , 0 otherwise xy fxy π +< = and this is pictured to the right. a) For 01 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
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 6

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online