An Introduction to Mathematical Statistics and Its Applications (6th Edition)
6th Edition
ISBN: 9780134114217
Author: Richard J. Larsen, Morris L. Marx
Publisher: PEARSON
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Chapter 13.3, Problem 1Q
Case Study 7.5.2 compared the volatility of Global Rock Funds’ return on investments to that of the bench-mark Lipper fund. But can it be said that the returns them-selves beat the benchmark? The table below gives the annual returns of the GlobalRock Fund for the years 1989 to 2007 and the corresponding Lipper averages. Test the hypothesis that
| Investment Return %Investment Return % | |||||
| Year | Global Rock, x | Lipper Avg., y | Year | Global Rock, x | Lipper Avg., y |
| 1989 | 15.32 | 14.76 | 1999 | 27.43 | 34.44 |
| 1990 | 1.62 | -1.91 | 2000 | 8.57 | 1.13 |
| 1991 | 28.43 | 20.67 | 2001 | 1.88 | -3.24 |
| 1992 | 11.91 | 6.18 | 2002 | -7.96 | -8.11 |
| 1993 | 20.71 | 22.97 | 2003 | 35.98 | 32.57 |
| 1994 | -2.15 | -2.44 | 2004 | 14.27 | 15.37 |
| 1995 | 23.29 | 20.26 | 2005 | 10.33 | 11.25 |
| 1996 | 15.96 | 14.79 | 2006 | 15.94 | 12.70 |
| 1997 | 11.12 | 14.27 | 2007 | 16.71 | 9.65 |
| 1998 | 0.37 | 6.25 | |||
Note that
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Pam, Rob and Sam get a cake that is one-third chocolate, one-third vanilla, and one-third strawberry as shown below. They wish to fairly divide the cake using the lone chooser method. Pam likes strawberry twice as much as chocolate or vanilla. Rob only likes chocolate. Sam, the chooser, likes vanilla and strawberry twice as much as chocolate. In the first division, Pam cuts the strawberry piece off and lets Rob choose his favorite piece. Based on that, Rob chooses the chocolate and vanilla parts. Note: All cuts made to the cake shown below are vertical.Which is a second division that Rob would make of his share of the cake?
Three players (one divider and two choosers) are going to divide a cake fairly using the lone divider method. The divider cuts the cake into three slices (s1, s2, and s3).
If the choosers' declarations are Chooser 1: {s1 , s2} and Chooser 2: {s2 , s3}.
Using the lone-divider method, how many different fair divisions of this cake are possible?
Theorem 2.6 (The Minkowski inequality)
Let p≥1. Suppose that X and Y are random variables, such that E|X|P <∞ and
E|Y P <00. Then
X+YpX+Yp
Chapter 13 Solutions
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
Ch. 13.2 - In recent years a number of research projects in...Ch. 13.2 - Prob. 2QCh. 13.2 - Prob. 3QCh. 13.2 - Prob. 4QCh. 13.2 - Prob. 5QCh. 13.2 - Prob. 6QCh. 13.2 - Prob. 7QCh. 13.2 - Prob. 8QCh. 13.2 - Prob. 9QCh. 13.2 - Prob. 10Q
Ch. 13.2 - Prob. 11QCh. 13.2 - Prob. 12QCh. 13.2 - Prob. 13QCh. 13.3 - Case Study 7.5.2 compared the volatility of Global...Ch. 13.3 - Recall the depth perception data described in...Ch. 13.3 - Useapaired t test to analyze the hypnosis/ESP data...Ch. 13.3 - Prob. 5QCh. 13.3 - Let D1,D2,...,Db be the within-block differences...Ch. 13.3 - Prob. 7QCh. 13.3 - Prob. 8QCh. 13.3 - Prob. 9Q
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