Suppose that when the radius of a circle is measured, an error is made that has a n(0, 2) distribution If n independent measurements are made, find an unbiased estimator of the area of the circle Is it best unbiased ...

X i nr 2 so nr 2 n and E 2 r 2 2 n Thu ...

Suppose that when the radius of a circle is measured, an error is made that has a

Question:

Suppose that when the radius of a circle is measured, an error is made that has a n(0, σ2) distribution. If n independent measurements are made, find an unbiased estimator of the area of the circle. Is it best unbiased?

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

1. When the radius of a circle increases and the magnitude of a central angle is held constant, how does the length of the intercepted arc change? Explain. 2. 3. A fan motor turns at a given angular...
If X is an unbiased measurement of a true value X, and U(X) is a nonlinear function of X, then in most cases U is a biased estimate of the true value U(X ). In most cases this bias is ignored. If it...
The radius of a circle is increasing at a rate of 2 ft min. At what rate is its area changing when the radius is 3 ft? (Recall that for a circle, A = r2.)
The Regina Company, Inc. BALANCE SHEET (In Thousands) ASSETS Cash Accounts Receivable Inventories Other Current Assets Total Current Assets Fixed Assets Accum Depreciation Other Assets TOTAL ASSETS...
Part 1 Goering, Zarcus, and Schmit are partners and share income and loss in a 3:2:5 ratio. The partnerships capital balances are as follows: Goering, $84,000; Zarcus, $69,000; and Schmit, $147,000....
Susan James, CPA is a partner in the firm of James and James that has several offices in New England/>. She is considering accepting Duke Company as an audit client. Under which of the following...
How do CRM and the use of databases in selling enhance closing and follow-up?
You are engaged by the owner of a small firm to recommend a one-year compensation contract for the firm's top manager. She is concerned about cash flow and feels that in previous years the manager...
Waterway Company's Assembly Department has materials cost of $3 per unit and conversion cost of $3 per unit. There are 19000 units in ending work in process inventory which are 80% complete as to...
Rocky Mountain Chocolate Factory manufactures an extensive line of premium chocolate candies for sale at its franchised and company-owned stores in malls throughout the United States. Its balance...
Let X1, X2, and X3 be a random sample of size three from a uniform(, 2) distribution, where > 0. (a) Find the method of moments estimator of . (b) Find the MLE, , and find a constant k such that...
Suppose that Xi, i = 1,..., n, are iid Bernoulli(p). (a) Show that the variance of the MLE of p attains the Cramer-Rao Lower Bound. (b) For n 4, show that the product X1X2X3X4 is an unbiased...
A plant is acquiring new production machinery. Before the machinery can be fully functional, a number of activities must be performed, including roughing out for power, placing the machinery,...
2.) As observed from the Earth, the intensity of sunlight is 1361 W/m. The permittivity of free space (the permittivity of the vacuum) is 8.854x10-12 F/m. Also, the permeability of free space (the...
Sum the two results to find the total displacement. LEARN MORE Remarks To find the displacement while braking, we could have used the two kinematics equations involving time, namely, Ax = vot + 1/2...
Calculate the Schwarzschild radius for the Sun. Here's what to do: 1 . Use M = 1 solar mass = _ _ _ _ _ _ kg , use the number you looked up in the previous problem. 2 . To get an answer in meters,...
A planet experiences a force of 2.65 x 1012 N from it's moon (mass of 2.77 x 1017 kg). If the moon is 3.05 x 109 m away from the planet and their radii can be neglected, what is the planet's mass? a....
The first questions are about estimates. Please see your class notes for details and remember: ( i ) an estimate is not a guess, and ( ii ) the best approach is to break down the problem into small...
For the following exercises, solve for x by converting the logarithmic equation to exponential form. log 3 (x) = 3
1. As a general strategy, would you recommend that Carl take an aggressive approach to capacity expansion or more of a wait-and-see approach? 2. Should Carl go with the option for one facility that...
Data were collected on the number of operating rooms in use at Tampa General Hospital over a 20-day period. On 3 of the days only one operating room was used; on 5 days, two were used; on 8 days,...
Shown is a probability distribution for the random variable x. x f(x) 3 .......0.25 6 ........0.50 9 .......0.25 Total 1.00 a. Compute E(x), the expected value of x. b. Compute 2, the variance of x....
Shown is a probability distribution for the random variable x. x f(x) 3 .......0.25 6 ........0.50 9 .......0.25 Total 1.00 a. Compute E(x), the expected value of x. b. Compute 2, the variance of x....
Excerpts from Andre Company's December 31, 2024 and 2023, financial statements are presented below: Accounts receivable Inventory Net sales Cost of goods sold Total assets Net income Total...
The York City Hospital has just acquired new equipment. The equipment cost $ 4 , 2 5 0 , 0 0 0 , and the organization spent $ 1 3 5 , 0 0 0 on upgrading the physical plant to the new equipment will...
Calculate the following showing all the necessary steps: Note: CPP rate to be used in the calculation is 5.95%. Note: Don't forget to deduct pay period exemption\ \ Tanya earns $25.00 per hour. This...

Suppose that when the radius of a circle is measured, an error is made that has a

Question:

Step by Step Answer:

X i nr 2 so nr 2 n and E 2 r 2 2 n Thu...View the full answer

Statistical Inference

Related Video

Students also viewed these Statistics questions