Question: Let X 1 , X 2 , ..., X n be a random sample from a population having mean and variance 2 . Consider the

Let X1, X2, ..., Xn be a random sample from a population having mean and variance 2. Consider the following estimators of .

1=(X1+2X2+X3)/4

2=(X1+X2-X3+4)/3

a)Calculate E[1]

b)Calculate E[2]

c)Calculate Variance (Var) [1]

d) Calculate Variance (Var) [2]

e)Determine the relative efficiency of 1 to 2

f) Which estimator is better? In what sense is it better?

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:

\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:

need full answer to attached question 3. Let X 1, X 2, . . . , X n be a random sample from a population with probability density function (26 i 1) 6 1 7 I9 fx(59;9) = (:6) 5'3 Find a Maximum...

Q:

Recall: k) In addition to many other wonderful services it provides, CourseCheggHero benets nancially from its customers' inability and/ or unwillingness to do their homework. Suppose that the time...

Q:

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...

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:

1. Let q; > 0 be a population parameter, and let X l , X 2, , X n be a random sample from a distribution with probability density function 2 105311) : 2 9K A, , x> 0. zero otherwise. m Recall: W = X2...

Q:

q: I need help with question 13, the picture attached, please! tell me if the question is not clear. 13. Let (X 15, X2011, 2' = 1, . - - , n, be iid random vectors from a bivariate normal...

Q:

Suppose the true model describing the relation between x and y is Where the εi are independently generated from a N (0, Ï2 i) distribution. Let Æ© be a matrix with...

Q:

Suppose the true model describing the relation between x and y is Where the εi are independently generated from a N (0, Ï2 i) distribution. Let Æ© be a matrix with...

Q:

Let X u...,Xn be a sample of size n from a normal population with mean v and variance a 2, and let Y x,...,Ym be a sample of size m from a normal population with mean v and variance a 2. Assume that...

Q:

Although each fraud is unique, there are commonalities among many of the major financial reporting frauds that have taken place in the past decade. What are the major commonalities and lessons that...

Q:

ABC Company is considering whether to open a new distribution center. The center would open January 1, 2015. To make the decision, the planning committee requires a master budget for the centers...

Q:

For a project to be suitable for project finance, which one of the following is NOT a basic characteristic required? Option A It should be stand - alone with a separately identifiable cash flow...

Q:

Diaz Company owns a milling machine that cost $126,300 and has accumulated depreciation of $91,000. Prepare the entry to record the disposal of the milling machine on January 3 under each of the...