GE 331-Lecture 23

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

This preview shows pages 1–9. Sign up to view the full content.

Final Time: 5/11/2009 Monday 1:30PM to 4:30PM Location: 1DCL-1310 1DCL-1320

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

View Full Document
1.Please print your name! 2.No more than 80 students in one classroom. 3.Please sign on the form when you come in
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)

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

View Full Document
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
u v u+v=2 u+v=1 1 1 2 2 0

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

View Full Document
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
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     

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

View Full Document
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
This is the end of the preview. Sign up to access the rest of the document.

## 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.

### Page1 / 18

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

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online