Let X 1 , X 2 , X 3 , , X n be a random sample with mean EX i , and variance Var(X i ) 2 Suppose that we use to estimate 2 Find the bias of this estimator 1 5 2 xr (2x ux) (X X) S k 1 k 1 nx...

Let X 1 , X 2 , X 3 , . . ., X n be a

Question:

Let X₁, X₂, X₃, . . ., X_n be a random sample with mean EX_i = μ, and variance Var(X_i) = σ². Suppose that we use 1 5--2-xr-|(2x-ux) (X X) = S k=1 k=1 nx

to estimate σ². Find the bias of this estimator -2 B(S) = E[S]0.

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

Step by Step Answer:

Related Book For book-img-for-question

Introduction To Probability Statistics And Random Processes

ISBN: 9780990637202

1st Edition

Authors: Hossein Pishro-Nik

See More Books

Question Posted: Oct 27, 2023 01:49 AM

See More Questions

Let X1, X2, . , Xn be a random sample of size n from a population with mean and variance 2. (a) Show that X2 is a biased estimator for 2. (b) Find the amount of bias in this estimator. (c) What...
Let X1, X2, . . . , Xn be a random sample from a gamma distribution with known and with = 1/. Say has a prior pdf that is gamma with parameters 0 and 0, so that the prior mean is 00. (a) Find the...
Let X1,.., Xn be a random sample from a population with mean Î¼ and variance Ï2. (a) Show that the estimator is an unbiased estimator of Î¼ if (b) Among all unbiased...
Two long wires are placed in the x-y plane, as shown in the figure. Each wire carries a current of 1.5 A, directed out of the page. If the distance d = 3.0 m, what is the net magnetic field due to...
1. Why did the Mississippi Supreme Court adopt the Texas duty of care for use in Mississippi? 2. Why did Mississippis highest court determine that Halls injury was foreseeable? 3. Why did the...
A pressurized spherical tank is made of 0.5-in.-thick steel. If it is subjected to an internal pressure of p = 200 psi, determine its outer radius if the maximum normal stress is not to exceed 15 ksi.
For Example 6.10, use a simulator to graph the effluent temperature of the methanol reactor as a function of the dodecane flow rate. Data From Example 6.10:- Data From Example 6.8:- Returning to...
At the beginning of the current season on April 1, the ledger of Five Pines Pro Shop showed Cash $3,000; Merchandise Inventory $4,000; and Irene Tiger, Capital $7,000.These transactions occurred...
A 38 kg crate rests on a floor. A horizontal pulling force of 170 N is needed to start the crate moving. 1.What is the coefficient of static friction between the crate and the floor? 2.The same crate...
Often when working with maximum likelihood functions, out of ease we maximize the log-likelihood rather than the likelihood to find the maximum likelihood estimator. Why is maximizing L(x; ) as a...
Let X 1 ,,X 4 be a random sample from an Exponential () distribution. Suppose we observed (x 1 ,x 2 ,x 3 ,x 4 ) = (2.35, 1.55, 3.25, 2.65). Find the likelihood function using as the PDF. fx; (x; 0) =...
Some experimental values of for argon gas at 1 atm are as follows: T, K: 300 400 500 600 700 800 , kg/m s: 2.27E5 2.85E5 3.37E5 3.83E5 4.25E5 4.64E5 Fit these values to either (a) A Power-law, or...
Write a method remove() that takes a linked-list Node and a string key as its arguments and removes every node in the list whose item field is equal to key.
Given a bitonic array of $n$ distinct integers, design a logarithmic-time algorithm to determine whether a given integer is in the array.
Modify BST to add a method size() that returns the number of key-value pairs in the symbol table. Use the approach of storing within each Node the number of nodes in the subtree rooted there.
Run experiments to validate the claims in the text that the put operations and get requests for Lookup and Index are logarithmic in the size of the table when using ST. Develop test clients that...
Central Appliance Center accumulates the following cost and net realizable value data at December 31. Compute the lower-of-cost-or-net realizable value for the companys total inventory. Inventory...
The following data are taken from the comparative balance sheets of Despina Company. Compute and interpret its accounts receivable turnover for year 2011 (competitors average a turnover of 7.5). 2010...
Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y = 2 - x if (x, y) = 6x + 3y + 3.
Drawing on data in Exhibit 3-4, do you think that Romania would be an attractive market for a firm that produces home appliances? What about Finland? Discuss your reasons.
Discuss the value of gross domestic product and gross national income per capita as measures of market potential in international consumer markets. Refer to specific data in your answer.
Discuss how the worldwide trend toward urbanization is affecting opportunities for international marketing.
b) Explain a man-in-the-middle attack. 13 Looking for physical address of a node with IP address 141.23.56.23 [4 MARKS] CHI System A Request B35 E Figure 1 System B c) Figure 1 shows an operation of...
The benefits and costs of increased security measures are difficult to quantify. For example, in real life, it is difficult to know for certain the probability of intercepting terrorists, and it's...
4. (24 points) IA32 Assembly (Procedure and Conditional Processing). For the following program, what are outputs for register EAX, EBX, ECX, and EDX in decimal? include Irvine32.inc .code main proc...

Let X 1 , X 2 , X 3 , . . ., X n be a

Question:

1 5--2-xr-|(2x-ux) (X X) = η S η k=1 k=1 nx

Step by Step Answer:

First note that Thus EX ...View the full answer

Introduction To Probability Statistics And Random Processes

Students also viewed these Business questions