GE 331-Lecture 23 - Final Time: 5/11/2009 Monday 1:30PM to...

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Final Time: 5/11/2009 Monday 1:30PM to 4:30PM Location: 1DCL-1310 1DCL-1320
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1.Please print your name! 2.No more than 80 students in one classroom. 3.Please sign on the form when you come in
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Quiz 7 A biased coin is tossed 80 times. Let p denote the probability of observing a Head. Suppose that the toss resulted in 49 HEADS and 31 TAILS. Find the maximum likelihood (ML) estimator of p. (Make sure you explain how you reached your decision to receive full credit)
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The joint probability density function   , , XY f u v for the continuous random variables X and Y has constant value on the shaded region : {(u, v) : 0 < u < 2, 0 < v < 2, 1 < u + v < 2} (a) Find   X fu , the marginal probability density function for X . (b) Find   | E Y X x , the conditional mean estimate of Y given X has been observed. Problem 1
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u v u+v=2 u+v=1 1 1 2 2 0
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u v u+v=2 u+v=1 dvdu v from 1-u to 2-u, u from 0 to 1 dvdu v from 0 to 2-u, u from 1 to 2 1 1 2 2 0 Region I Region II
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find the joint pdf, we know it is a constant, then assume   , , XY f u v c , then we have   , I and II I and II 1 2 2 2 0 1 1 0 , 33 1 2 1 22 2 3 region region u v u u v u u v u u v f u v dvdu cdvdu cdvdu cdvdu c c c                  Thus we have   , 2 ,0 2,0 2,1 2 , 3 0, u v u v f u v otherwise     
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u v u+v=2 u+v=1 dudv u from 0 to 2-v, u from 1 to 2 dudv u from 1-v to 2-v, v from 0 to 1 1 1 2 2 0 Region I Region II
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This note was uploaded on 09/08/2009 for the course GE 331 taught by Professor Negarkayavash during the Spring '09 term at University of Illinois at Urbana–Champaign.

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GE 331-Lecture 23 - Final Time: 5/11/2009 Monday 1:30PM to...

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