Let X1, , Xn be a random sample from a population with mean Icirc frac14 and variance Iuml 2 (a) Show that the estimator is an unbiased estimator of Icirc frac14 if (b) Among all unbiased estimators of this form (called linear unbiased estimators) find the one with minimum variance, and calculate t...

a E i a i X i i a i EX i i a i i a i Hence the estimator is unbiased b Var i a i X i i ...

Let X1,.., Xn be a random sample from a population with mean Î¼ and variance Ï2. (a)

Question:

Let X1,.., Xn be a random sample from a population with mean Î¼ and variance Ïƒ2.
(a) Show that the estimator

is an unbiased estimator of Î¼ if

(b) Among all unbiased estimators of this form (called linear unbiased estimators) find the one with minimum variance, and calculate the variance.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Statistical Inference

ISBN: 978-0534243128

2nd edition

Authors: George Casella, Roger L. Berger

See More Books

Question Posted: May 26, 2016 05:25 AM

See More Questions

Let X1, . . ., Xn be a random sample from a population with mean m and variance 1. Show that -cap2 = X-bar2 is a biased estimator of 2, and compute the bias.
Let X1, . . ., Xn be a random sample from a population with pdf Find a method of moments estimator for . 0, otherwise.
Let X 1 , . . ., X n be a random sample from a population with density (a) Show that X-bar is a biased estimator of . (b) Show that X-bar is an unbiased estimator of = 1 + . f(x)-( e -(1-9 , forx >
Consider a social network where people are represented as vertices and friendships as edges. If there are 1 0 people in the network and each person is friends with 3 others, calculate the total...
Part 1. Gibbs, Mier, and Hill are partners and share income and loss in a 5:1:4 ratio. The partnerships capital balances are as follows: Gibbs, $303,000; Mier, $74,000; and Hill, $223,000. Gibbs...
Submit a paper naming the four major outlaw motorcycle gangs that operate in the United States and discuss the structure of their organizations as well as the similarities between them.
Complete the priority checklist in Exhibit 10.2. What do your responses to the checklist tell you about your career choices? Personal Life Family Life goals Personal wealth Career Goals Ambition...
Peach Corporation (a calendar year company) recorded the following transactions. Taxable income ...................... $5,000,000 Regular tax depreciation on realty in excess of ADS (placed in...
Make a linear graph of your experimental data Moving Tension experimental (y-axis) vs. Moving Tension predicted (x-axis). What is the slope m and the slope's uncertainty of your graph? Report your...
The PM Computer Company makes build-to-order (BTO) computers at its distribution center year round. The following table shows the average value (in $ millions) of component parts, work-in-process,...
Let X1,..., Xn be iid Bernoulli(p). Show that the variance of attains the Cramer-Rao Lower Bound, and hence is the best unbiased estimator of p.
Exercise 7.42 established that the optimal weights are q*i = (1/Ï2i)/(j 1/Ï2j). A result due to Tukey (see Bloch and Moses 1988) states that if W = i qiWi is an estimator based on another...
Describe the set of antiderivatives of f(x) = 0.
We have seen that MM1 with taxes and bankruptcy costs is written S + B = S0 + T S P VBC , where S is the levered firm's value of equity, B is the levered firm's value of debt, S0 is the unlevered...
Evaluating Corporate Social Responsibility - Corporate Social Responsibility 1 STARBUCKS https://www.starbucks.com/responsibility/global-report...
B Inc. has ne income of $30,000 for the current year, including dividends received from taxable Canadian corporations of $2,000 and taxable capital gains of $3,000. B Inc. donated $25,000 to a...
Investing activities on the statement of cash flows include buying equipment that is held for long - term use. True False
Consider the representative investment in the venture capital fund shown in the worksheet "VC Fund I" in the student spreadsheet file. Assume that the FoF or Investure commits $7.5 million to VC Fund...
For the following exercises, use the definition of a logarithm to rewrite the equation as an exponential equation. log (100) = -2
A supermarket chain is interested in exploring the relationship between the sales of its store-brand canned vegetables (y), the amount spent on promotion of the vegetables in local newspapers (x1)...
An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities. P(high-quality oil) = 0.50 P(medium-quality oil) = 0.20 P(no oil) = 0.30...
An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities. P(high-quality oil) = 0.50 P(medium-quality oil) = 0.20 P(no oil) = 0.30...
Small cars get better gas mileage, but they are not as safe as bigger cars. Small cars accounted for 18% of the vehicles on the road, but accidents involving small cars led to 11,898 fatalities...
Image transcription text 1. A cylindrical specimen of cold-worked copper (see Fig. below) has experienced a ductility of 25%EL. If its cold worked radius is 10 mm, what was its radius before...
Question 2 As a project manager, you need to synthesize information about a problem to stakeholders. What should you do first in your synthesizing process? Describe Briefly.
Please help me as much as you can!! I will take all your effort to solve this problem and will give you a good rate!!! Please show all the calculations in detail! Also, please do not copied and...

Let X1,.., Xn be a random sample from a population with mean Î¼ and variance Ï2. (a)

Question:

ai = 1. al-

Step by Step Answer:

a E i a i X i i a i EX i i a i i a i Hence the estimator is unbiased b Var i a i X i i ...View the full answer

Statistical Inference

Students also viewed these Statistics questions