(a) For random variables X and Y , show that Cov(X + Y, X Y )...

Question:

(a) For random variables X and Y , show that
Cov(X + Y, X − Y ) = Var(X) − Var(Y)
(b) Suppose that Cov(X, Y) = 0. Prove that
ρ(X + Y, X − Y ) = Var(X) − Var(Y)/Var(X) + Var(Y)

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

Step by Step Answer:

Related Book For book-img-for-question

Introduction To Mathematical Statistics And Its Applications

ISBN: 9780321693945

5th Edition

Authors: Richard J. Larsen, Morris L. Marx

See More Books

Question Posted: Dec 20, 2015 03:48 AM

See More Questions

The managing partner for Westwood One Investment Managers, Inc., gave a public seminar in which she discussed a number of issues, including investment risk analysis. In that seminar, she reminded...
(a) Show that for random variables X and Y and constants a, b, c, d, Cov(ay + bX, cY + dX) = acVar Y + (be + ad)Cov(X, Y) + bdVar X. (b) Use the result in part (a) to verify that in the structural...
For correlated random variables X and Y it is natural to ask for the expected value for X given Y . For example, Galton calculated the expected value of the height of a son given the height of the...
On December 31, 2021, L Inc. had a $1,600,000 note payable outstanding, due July 31, 2022. L borrowed the money to finance construction of a new plant. L planned to refinance the note by issuing...
The Economic Growth and Tax Relief Reconciliation Act of 2001 (EGTRRA) lowered the top marginal rate for estate taxation, called for a gradual increase in the estate tax exemption (the amount of an...
Decision-makers use accounting information in a wide variety of decisions including the following: 1. Deciding whether or not to lend money to a business 2. Deciding whether or not an individual has...
Assume there exists a return R that is on the mean-variance frontier and is an affine function of a vector F; that is, R = a + b F. Assume either (i) there is a risk-free asset and R = Rf , or...
APCO Company manufactures various lines of bicycles. Because of the high volume of each line, the company employs a process cost system using the weighted-average method to determine unit costs....
Tops Corporation is organized into two divisions, Manufacturing and Marketing. Both divisions are considered to be profit centers and the two division managers are evaluated in large part on...
Company A is involved in the construction industry and was founded in 1976. It is listed on Bursa Malaysia's main market as Company A is involved in the construction industry and was founded in 1976....
Let the random variable X take on the values 1, 2, . . . , n, each with probability 1/n. Define Y to be X 2 . Find (X, Y) and (X, Y ). im
Derive Equation 11.4.2 from Equation 11.4.1. i-1 i-1
Explain why a plain vanilla interest rate swap and the compounding swap in Section 34.2 can be valued using the "assume forward rates are realized" rule, but a LIBOR-in-arrears swap in Section 34.4...
Admin Support Cereal Bars Square Foot 1,250 1,500 7,500 7,000 # of employees 14 11 42 59 # of machine batches 0 0 14 27 # of computers 17 21 35 30 Costs 32,000.32 21,740.21 The Support department...
Compare and contrast the differences between innovation and creativity. Does one lead to the other? If so, please explain. Why is innovation important? Who within the organization is responsible for...
Using the tables from Check your Consumer Surplus and Producer Surplus activities, find the equilibrium price and quantity in the market for cheese-stuffed jalapeno peppers. What is the total surplus...
We decided to use Gehan's two-stage design for this purpose. In the first stage, we will discard the new treatment if no patient out of n0 patients. Suppose the probability we can tolerate to discard...
Claude Haridge was involved in a demonstration. He threw a paint balloon at a bus and some of the paint flecks hits a nearby officer, so Haridge was transported to police cells. At the cells Special...
Describe activity crashing and solve typical problems.
Use the information given about the angles and to find the exact value of: (a) sin( + ) (b) cos( + ) (c) sin( - ) (d) tan ( + ) (e) sin(2) (f) cos (2) (g) sin /2 (h) cos/2 cos = 4/5, 0 < < /2; cos =...
Why is it important that the proper amount be assigned to inventory? a. Because the amount assigned to inventory will affect the amount eventually recorded as cost of goods sold. b. Because the...
Let X1, X2, .. , X7 denote a random sample from a population having mean and variance. Consider the following estimators of μ: (a) Is either estimator unbiased? (b) Which estimator is best? In...
Suppose that Ф1 and Ф2 are unbiased estimators of the parameter . We know that V (Ф1) = 10 and V(Ф2) = 4. Which estimator is best and in what sense is it best?
Calculate the relative efficiency of the two estimators in Exercise 7-2.
Current Portion of Long-Term Debt PepsiCo, Inc., reported the following information about its long-term debt in the notes to a recent financial statement (in millions): Long-term debt is composed of...
Show transcribed image text 31/12/2016 GHS'000 25,500 The following information relates to the draft financial statements of Samanpa Ltd. Summarised statement of financial position as at: 31/12/2017...
\ How do i solve this? Beginning raw materials inventory Ending raw materials inventory Direct labor Operating expenses Purchases of direct materials Beginning work in process inventory Ending work...

(a) For random variables X and Y , show that Cov(X + Y, X Y )...

Question:

Step by Step Answer:

a CovX Y X Y EX YX Y EX YEX Y EX 2 Y 2 X ...View the full answer

Introduction To Mathematical Statistics And Its Applications

Students also viewed these Statistics questions