# hw2_1 - Homework 2(due Feb 1 1 Which of the following...

• Notes
• nizhes
• 1

This preview shows page 1. Sign up to view the full content.

Homework 2 (due Feb. 1) 1. Which of the following statistics are unbiased estimators for the pop- ulation mean μ ? For those which are not unbiased, find the bias. a) X 1 + X 3 2 b) X 1 + X 3 + X n 3 c) X 1 + X 3 +3 X 2 - X 4 5 d) 3 X 1 - 2 X 3 e) X 1 - X 2 + X n/ 2 - X n - 1 + X n 2. For the estimators in problem 1, find their mean square error. Which appears to be the most efficient one (with the smallest MSE) if the standard deviation of the population is equal to its mean (
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: σ = μ )? 3. Consider the Poisson distribution f ( x ) = e-λ λ x x ! , x = 0 , 1 , 2 ,... Find the maximum likelihood estimator or λ , based on a random sample of size n . 4. Suppose the size n sample comes from a distribution uniform on the interval [ a,b ] with both a and b unknown parameters. Find the MLE for a and b . 1...
View Full Document

• Spring '08
• Perevalov
• Normal Distribution, maximum likelihood estimator, mean square error, Bias of an estimator, unbiased estimators

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern