Question: Let A(X) = E(| X E(X) |), the expected value of the absolute value of the deviation of X, where X is a random

Let A(X) = E(| X − E(X) |), the expected value of the absolute value of the deviation of X, where X is a random variable. Prove or disprove that A(X + Y) = A(X) + A(Y) for all random variables X and Y.

Step by Step Solution

★★★★★

3.42 Rating (152 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

This is certainly not true if X and Y are not independent For exa... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

923-M-C-M-S (2122).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Let the random variable X denote a measurement from a manufactured product. Suppose the target value for the measurement is m. For example, X could denote a dimensional length, and the target might...

Let X, Y, and Z be independent random variables, each with mean and variance 2. (a) Find the expected value and variance of S = X + Y + Z. (b) Find the expected value and variance of A = (1/3) (X + Y...

16. Let X have the negative binomial distribution with parameters r and p. Thus, X counts the total number of Bernoulli trials until the rth success. Next, let X1 denote the number of trials up to...

board urses 18 lendar E Inbox > 1 2 D 3 D 4 History 5 ? Help 6 7 1 Excel Project 2 Please download the Excel file and use it to work on the following questions. Excel Project 2.xlsx This assignment...

Part 2 (Theoretical Analysis): Compute the expected value, variance, and standard deviation of the random variable X. See the additional notes for discussion on these computations, in brief: P(X=i) =...

6. Let A = {x E Z |x 2 5a + 2 for some integer a}, B = {y E Z | y = 10!) 3 for some integer b}, and C = {z E Z | z = 106 + 7 for some integer C}. Prove or disprove each of the following statements....

STAT 1222 Spring 2012 Common Final Exam May 3, 2012 Please print the following information: Instructor: Name: Student ID #: Section/Time: THIS EXAM HAS TWO PARTS PART I. Consists of 30 multiple...

All questions. 05:50:42 VA; 25% ' ASSIGNMENTNM1.pdf IQ 0+ Numerical Methods-Assignment-l Mathematical Prelimanaries, Taylor's Theorem, Order of Convergence (1) Let L be a real number and let {an} be...

Hidden Markov models (HMM) are widely used in Bioinformatics. (i) In a HMM when would you use the Baum-Welch algorithm, and when the Viterbi algorithm, and why? Give biologically motivated examples....

Prove that the function. f(x) = 1 = 12 is where but no where every Continuous differentiable except at the origin.

If you were a management accountant at a company and the cost of goods manufactured (being 2,349,000) and the income statement was (1,773,000). How would you analyze the results for both outcomes to...

The competitive market provides the best outcome for society because (A) consumer surplus is minimized, while producer surplus is maximized. (B) the total welfare is maximized. (C) producer surplus...

Suppose the price elasticity of demand for used cars is estimated to be 3. What does this mean? What will be the effect on the quantity demanded for used cars if the price rises by 10 percent?

Suppose that we have assumed the straight-line regression model Y = BO + B1X1 + but the response is affected by a second variable x2 such that the true regression function is E(Y) = BO + B1X1 + B2X2...

Suppose that we are fitting a line and we wish to make the variance of the regression coefficient B1 as small as possible. Where should the observations xi, i = 1, 2, p, n, be taken so as to minimize...

Weighted Least Squares suppose that we are fitting the line Y = Bo + B1x + , but the variance of Y depends on the level of x; that is, where the wi are constants, often called weights. Show that for...

Answer the 4 questions below based on the following information. Taxes are 35% and all dollars are in millions. Calculate each company's ROE, ROA, and ROIC. Please provide calculations. Why is...

Moving to another question will save this response Question 20 of 27 Question 20 2 points On July 10, 2012, you purchase a $10,000 par T-note that matures in five years. The settlement occurs on July...

Metallica Bearings, Incorporated, is a young start-up company. No dividends will be paid on the stock over the next nine years because the firm needs to plow back its earnings to fuel growth. The...