2018Review-1.pdf - MFIN 6603(A&B Review Problems 1 Aydede/Dar Question 1 Consider a sample of size N on variables X and Y Establish whether each of the

# 2018Review-1.pdf - MFIN 6603(A&B Review Problems 1...

• 2

This preview shows page 1 - 2 out of 2 pages.

MFIN 6603 (A &B) Aydede/Dar Review Problems 1 October 31, 2018 Question 1 Consider a sample of size N on variables X and Y. Establish whether each of the following is TRUE or FALSE. i. If the constants a and b are the sample means of X and Y respectively, (x i a)(y i b)= x i y i nab. ii. Under the conditions stated in ii ., Σ(x i a) = Σ(y i b) = 0. iii . (x i a) 2 = x i 2 Na 2 only if a is the sample mean of X. iv. ax i / a = . v. a i x i / a i = x i . vi. cov(a + bX+ cZ, Y)= b cov(X,Y) + c cov(Z,Y) Question 2 Suppose X and Y are two random variables for whom E(X)=5, E(Y)=2, var(X)=10, var(Y)=20, and cov(X,Y)=5. Consider then the following two linear functions of X and Y: A=2X + Y and B=X-2Y. (i) Find the means and variances of A and B, and show that E(AB)= 2E(X 2 )-2E(Y 2 ) -3E(XY). (iii) Suppose X*=10 +2X and Y*=10-2Y, find cov(X*,Y*). Question 3 The table below gives the joint probability distribution of two important macroeconomic aggregates: the investment rate X (the amount of investment in physical capital relative to GDP), and the growth rate of the economy Y, measured by the rate of growth of real GDP, both in percent. GDP Growth Rate Y (%) Investment Rate X (%) -2 0 5 10 5 0.10 0.10 0 0 10 0.01 0.08 0.10 0.05 20 0 0.04 0.10 0.10 30 0 0 0.12 0.20 A. Find the marginal distributions, and then calculate the means and variances of X and Y. B. Determine the conditional distributions of growth f(Y|X) and then calculate their means. What conclusion (if any) can you draw from the conditional means?) C. Find the covariance ( σ̂ xy

• Fall '14
• Staff

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern