Homework Help is Here – Start Your Trial Now!
Math
Statistics
Using a long rod that has length m, you are going to lay out a square plot in which the length of each side is m. Thus the area of the plot will be m2 . However, you do not know the value of m, so you decide to make n independent measurements X1, X2,... Xn of the length. Assume that each Xi has mean m (unbiased measurements) and variance s2 . a. Show that X2 is not an unbiased estimator for m2 . [Hint: For any rv Y, E(Y2 ) ¼ V(Y) + [E(Y)]2 . Apply this with Y ¼ X.] b. For what value of k is the estimator X2 - kS2 unbiased for m2 ? [Hint: Compute E(X2 - kS2).]

Using a long rod that has length m, you are going to lay out a square plot in which the length of each side is m. Thus the area of the plot will be m2 . However, you do not know the value of m, so you decide to make n independent measurements X1, X2,... Xn of the length. Assume that each Xi has mean m (unbiased measurements) and variance s2 . a. Show that X2 is not an unbiased estimator for m2 . [Hint: For any rv Y, E(Y2 ) ¼ V(Y) + [E(Y)]2 . Apply this with Y ¼ X.] b. For what value of k is the estimator X2 - kS2 unbiased for m2 ? [Hint: Compute E(X2 - kS2).]

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question

Using a long rod that has length m, you are going
to lay out a square plot in which the length of each
side is m. Thus the area of the plot will be m2
.
However, you do not know the value of m, so
you decide to make n independent measurements
X1, X2,... Xn of the length. Assume that each Xi
has mean m (unbiased measurements) and variance s2
.
a. Show that X2 is not an unbiased estimator
for m2
. [Hint: For any rv Y, E(Y2
) ¼
V(Y) + [E(Y)]2
. Apply this with Y ¼ X.]
b. For what value of k is the estimator X2 - kS2
unbiased for m2
? [Hint: Compute E(X2 - kS2).]

Expert Solution
Step 1

Given:

The Area of the plot = m2

Independent measurements = n

Mean = m

Variance = s2

trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS