Question: Let X 1, X 2,..., Xn be a random sample from any distribution with mean and variance 2. Consider the following two unbiased estimators of

Let X1, X2,..., Xn be a random sample from any distribution with mean and variance 2.

Consider the following two unbiased estimators of .

hat 1=X bar

and

hat 2 = X1/3 + 2(X2+X3++Xn) /3(n-1)

Find the efficiency of hat 1 relative to hat 2.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
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 Mathematics Questions!

Q:

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...

Q:

Let X 1 , X 2 , X 3 , . . ., Xn be a random sample from a distribution with mean EX i = , and variance Var(X i ) = 2 . Consider the following two estimators for : Find MSE(^ 1 ) and MSE(^ 2 ) and...

Q:

Let X1. X2, Xn be a random sample from a distribution with mean u and variance (:2. Consider the random variable. X. Which of the following properties are true? Select all that apply. On average, the...

Q:

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...

Q:

7. Let X 1 , X 2 , ... , Xn be i.i.d. N(B, a 2 ), a 2 known. Consider the following class of conjugate priors forB: r = { N(O, 7 2 ), 7 2 > 0 }. (a) Find the range of posterior means. (b) Find the...

Q:

Q6. Suppose that X =61 + 52, where 1 N N(6,1), 52 ~ N()\\6', A2), and 1 and 52 are in- dependent. Here, A 2 1 is a given constant, and 6 is a unknown parameter. (iv) Let X 1, X 2, - - - ,Xn be an...

Q:

\f 1 Let X 1 , X 2 ,....., X n is a random sample from a normal distribution with mean and variance 02 known. Then probabilily density function 1 x i 2 0 1 f xi 2 e , xi , 0, 0 2 By def, Likelihood...

Q:

ANSWER THESE QUESTIONS USING TRUE OR FALSE: a. Gauss's Law describes the relationship between the net electric flux through a closed surface and the charge enclosed INSIDE the surface. b. Gauss's Law...

Q:

Let X1,X2, ,Xn be a random sample from a distribution with pdf f(x;), where is an unknown parameter. T(X1,X2, ,Xn) is a function of X1,X2, ,Xn used to estimate . Explain the meaning of: (i) T(X1,X2,...

Q:

2 STAT 330: Mathematical Statistics Winter 2016 Assignment 3 Name: ID: Due on March 28th (Monday) 11:30am in drop boxes across the hall from MC 4065/4066. 1 1. [6 marks] Suppose X1 , X2 , . . . are...

Q:

In each of the following cases, do you think the sample size is large enough to use the normal distribution to make a test of hypothesis about the population proportion? Explain why or why not. a. n...

Q:

Suppose a group of high school friends work at the same fast-food restaurant. They all dislike the manager because she doesnt allow them to swap shifts with one another whenever someone has a big...

Q:

17.4 What is artificial intelligence, and what is its relationship to machine learning?

Q:

Please help it's urgent thank you. please write 400-450 words. thank you QUESTION 4 (20 MARKS) The success of any project is dependent on a diverse range of skills, abilities and competencies of the...

Q:

Keep your head straight on your shoulders

Q:

Be straight in the back without blowing out the chest

Q:

Wear as little as possible