If X 1 and X 2 are the means of independent random samples of sizes n 1 and n 2 from a normal population with the mean and the variance 2 , show that the variance of the unbiased estimator Is a minimum when n 1 n 1 n 2 X (1 w) X2...

If X 1 and X 2 are the means of independent random samples of sizes n 1

Question:

If X̅₁ and X̅₂ are the means of independent random samples of sizes n₁ and n₂ from a normal population with the mean µ and the variance σ², show that the variance of the unbiased estimator

Is a minimum when ω = n₁ / n₁ + n₂

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

Step by Step Answer:

Related Book For book-img-for-question

John E Freunds Mathematical Statistics With Applications

ISBN: 9780134995373

8th Edition

Authors: Irwin Miller, Marylees Miller

See More Books

Question Posted: Nov 04, 2015 03:32 AM

See More Questions

One property of the mean is that if we know the means and sample sizes of two (or more) data sets, we can calculate the combined mean of both (or all) data sets. The combined mean for two data sets...
The data for a random sample of six paired observations are shown in the next table. a. Calculate the difference between each pair of observations by subtracting observation 2 from observation 1. Use...
Two independent random samples of sizes n1 = 4 and n2 = 5 are selected from each of two normal populations: a. Calculate s2, the pooled estimator of s2. b. Find a 90% confidence interval for (1 - 2),...
2) WWW.myitlab.com is an example of a(n). O domain name O protocol prefix OURL omni box
The employees at a General Motors assembly plant are polled as they leave work. Each is asked, What brand of automobile are you riding home in? The random variable to be reported is the number of...
Given below is an important figure, Kate Middleton, who wore earrings of Pakistani brand (Zeen) during her visit in Pakistan Explain how this would influence the buying behavior of consumers?
Bill Beck, Bruce Beck, and Barb Beck formed the BBB Partnership by making capital contributions of $67,500, $262,500, and $420,000, respectively. They predict annual partnership net income of...
Prepare the monthly income statement, monthly statement of owners equity, and the balance sheet at August 31, 2014, for Krishna Cleaning Company from the data provided in the adjusted trial balance...
Imagine that while cleaning out your great-grandfather's attic, you find a rucksack containing a journal and a sheaf of papers. Your great-grandfather, a noted entrepreneur and businessman, was also...
Consider the following traffic flow diagram, where a1, a2, a3, a4, b1, b2, b3, b4 are fixed positive integers. Set up a linear system in the unknowns x1, x2, x3, x4 and show that the system will be...
With reference to Exercise 10.21, find the efficiency of the estimator of part (a) with Ï = 1/2 relative to this estimator with In exercise If 1 is the mean of a random sample of size n from a...
With reference to Exercise 10.23, find the efficiency of the estimator with = 1/2 relative to the estimator with = n 1 / n 1 + n 2 .
The financial statements of P Co and its subsidiaries and associate are shown below: Additional information 1. Intangible assets of B Co had an indefinite useful life. On 31 December 20x6, the annual...
CLT HW Score: 0/19 0/19 answered Question 4 < = 31. You intend to draw a A population of values has a normal distribution with = 232.9 and random sample of size n = 165. Please show your answers as...
Q-3: Estimate fxy dx + x2 dy: where c is given by [Hint: Use Green's theorem -1
1. Determine completely the resultant of the four forces shown in the figure. Each force makes a 15 angle with the vertical, except the 200 N force which is vertical. Find the action line (position)...
1: Based on the results of your Learning Style produce a 1 pg reflection. (this is the result of the test i took: Your learning preference:Multimodal (AK) SharePeople with your preference like:...
Explain what the petty cashier should do if he or she thinks that the imprest amount is inadequate.
Go to www.acq.osd.mil/evm and explore the various links and screens. What does the size and diversity of this site tell you about the acceptance and use of earned value in organizations today?
we have to compute the letter grades for a course. The data is a collection of student records stored in a file. Each record consists of a name(up to 20 characters), ID (8 characters), the scores of...
Proha Company acquired all of Sonara Company's voting stock for $$40$ million cash. The book value of Sonara's net assets on that date was $$8$ million. The book values of Sonara's individual...
Each month a brokerage house studies various companies and rates each companys stock as being either low risk or moderate to high risk. In a recent report, the brokerage house summarized its findings...
John and Jane are married. The probability that John watches a certain television show is .4. The probability that Jane watches the show is .5. The probability that John watches the show, given that...
In Exercise 4.20, find the probability that either John or Jane watches the show. In Exercise 4.20 John and Jane are married. The probability that John watches a certain television show is .4. The...
XF Ltd. Is an expanding private company in the electric trade. Accounts preparing in January 2019 included the following information: Profit Statement for the year ended 31 st December 2018 Kshs.000...
Check On June 15, 2021, Sanderson Construction entered into a long-term construction contract to build a baseball stadium in Washington D.C., for $340 million. The expected completion date is April...
Q.1 Bassem Company purchased OMR420,000 in merchandise on account during the month of April, and merchandise costing OMR $350,000 was sold on account for OMR 425,000. Required: 1. Prepare journal...

If X 1 and X 2 are the means of independent random samples of sizes n 1

Question:

.X+(1-w) X2

Step by Step Answer:

var w 2 2 n 1 1 w 2 ...View the full answer

John E Freunds Mathematical Statistics With Applications

Students also viewed these Statistics questions