Question: Let y 1 , y 2 , y 3 , . . . , y n be a random sample from a Poisson distribution with

Let y₁, y₂, y₃, . . . , y_n be a random sample from a Poisson distribution with mean λ, i.e., E (y_i) = λ, i = 1, 2, .... n. Consider four estimators of λ:

A2 = n(y, + y2 + .+ yn) %3D y + y2

a. Which of the four estimators are unbiased?
b. Of the unbiased estimators, which has the smallest variance? Recall that, for a Poisson distribution, V(y_i) = λ.

A2 = n(y, + y2 + .+ yn) %3D y + y2

Step by Step Solution

★★★★★

3.47 Rating (176 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a To determine if an estimator is unbiased we need to check if its expected value is equal to the tr... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Statistics For Engineering And The Sciences Questions!

Let X1,..., Xm be a random sample from a Poisson distribution with parameter µ1, and let Y1,..., Yn be a random sample from another Poisson distribution with parameter µ2. We wish to test...

Let Xi,..., Xn be a random sample from a population with mean fi and variance Ï2. Show that Thus, the normalization of X-n in the Central Limit Theorem gives random variables that have the same...

Let X1,.., Xn be a random sample from a population with mean Î¼ and variance Ï2. (a) Show that the estimator is an unbiased estimator of Î¼ if (b) Among all unbiased...

please help me with questions 8 and 9. I also need help with number 5 from c-f. Page 4 of 4 ZOOM + 8. 9. 10(points) Let X 1, X2, X3, ...,Xn be a random sample that have exponential distribution with...

I need help with number 5 and 8 please Page 4 of 4 ZOOM + 8. 9. 10(points) Let X 1, X2, X3, ...,Xn be a random sample that have exponential distribution with parameter A. a) Find the method of...

I need help with number 8 and 5 Page 4 of 4 ZOOM + 8. 9. 10(points) Let X 1, X2, X3, ...,Xn be a random sample that have exponential distribution with parameter A. a) Find the method of moments...

13. (Box (1980)) Let X 1 , X 2, , Xn be a random sample from N (e, a-2 ) with both e and cr2 unknown. It is of interest to detect discrepancy in the variance of the model with the target model...

INFERENCE STATISTICS QUESTION 3 Let X 1, X 2, ..., Xn be a random sample of at annual rainfall measurements in RSA. Furthermore, suppose that the distribution of the annual rainfall in RSA has...

STA5326 - Mathematical Statistics - II Homework # 3 1. If X 1 , X 2 ,..., X n is a random sample of size n from N ( , 2 ), , show that n n n 2 2 X j , X j or X , X j = = j 1 j 1 =j 1 is a sufficient...

Hello, I am stuck on all three parts of this question (as shown in the attached picture). Please help explain, thank you! 1. Let X = (X1, X 2, , X\") be a random sample, where X 1- is a Poisson...

A large refrigeration plant is to be maintained at - 15oC, and it requires refrigeration at a rate of 100 kW. The condenser of the plant is to be cooled by liquid water, which experiences a...

Explain why the carbon atom (Z = 6) usually forms four bonds with hydrogen-like atoms.

Which of the following best defines a scenario analysis? Multiple Choice The determination of changes in NPV estimates when what - If questions are posed. The isolation of the effect that a single...

7. Communication may be helped or hindered when a. proper grammar is used b. language is used in unique or unusual ways c. clichs are avoided d. sexist or ageist language is utilized

f. Given that the shirt just sold was a medium plaid, what is the probability that it was short-sleeved? Long-sleeved?

51. One box contains six red balls and four green balls, and a second box contains seven red balls and three green balls. A ball is randomly chosen from the first box and placed in the second box....

52. A system consists of two identical pumps, #1 and #2. If one pump fails, the system will still operate. However, because of the added strain, the extra remaining pump is now more likely to fail...

answer with explanation in your own words and dont copy paste QUESTION 7 Sabrina wants to know how the other students at her school view the occult. She asks her friends who are in the Wiccan club...

Question 2 (3 Marks) Anna is a Vice President at the J Corporation. The company is considering investing in a new factory and Anna must decide whether it is a feasible project. In order to assess the...

You have an opportunity to invest $ 1 0 8 0 0 0 now in return for $ 7 9 5 0 0 in one year and $ 3 0 comma 3 0 0 in two years. If your cost of capital is 8 . 5 % , what is the NPV of this investment?...