Assignment Rules
Homework assignments must be typed. For instruction on how to type equations and math objects please see notes “Typing Math in MS Word”.
Homework assignments must be prepared within this template. Save this file on your computer and type your answers following each question. Do not delete the questions.
Your assignments must be stapled.
No attachments are allowed. This means that all your work must be done within this word document and attaching graphs, questions or other material is prohibited.
Homework assignments must be submitted at the end of the lecture, in class, on the listed dates.
Late homework assignments will not be accepted under any circumstances, but the lowest homework score will be dropped.
The first homework assignment cannot be dropped.
You are encouraged to collaborate on all homework assignments by discussing the problems with each other, but submitted work must be your own. Sharing the electronic version of your assignment with other students is absolutely prohibited.
All the graphs should be fully labeled, i.e. with a title, labeled axis and labeled curves.
In all the questions that involve calculations, you are required to show all your work. That is, you need to write the steps that you made in order to get to the solution.
This page must be part of the submitted homework.
Properties of Estimators
Define the following concepts:
Random Sample.
Estimator.
Estimate.
Suppose is an estimator of the population mean , with being numbers.
Prove that this estimator is unbiased if and only if .
Prove that if , then the estimator is efficient among all unbiased estimators of the form .
Suppose A and B are two estimators, with the following properties:
A
B
Bias
-2
1
Variance
5
8
Based on our definition of efficient estimator, can we determine which of these two estimators is more efficient?
Based on the MSE criterion, which estimator would you choose?
The following are estimators of the population…