The following are hypothetical data for the U.S. balance of payments. Use the data to calculate each of the following (assume credit balances):
a.Merchandise trade balance
b.Balance on goods and services
c.Balance on current account
d.Financial account balance
e.Statistical discrepancy
Billions of Dollars
Merchandise exports350.0
Merchandise imports2,425.0
Service exports2,145.0
Service imports170.0
Net income and net transfers221.5
Outflow of U.S. capital245.0
Inflow of foreign capital100.0
What are the Sum of Square between (SSB) and Sum of Squares within (SSw)? SSB = 1041 SSw = 1003 O SSB = 1003 SSw = 1041 O SSB = 1041/2 = 520.5 SSw = 1003/27 = 37.1 O SSB = 1003/27 = 37.1 SSw = 1041/2 = 520.52 3-i For matrix given by H = 3+i -1 answer questions 7 - 10 7 - Is H Hermitian? 8 - Find the Eigen-values of H. 9 - Find the Eigen-vectors of H. 10 - Find the transformation matrix U and show that it is unitary. Evaluate the following matrix product U-1HU.(Question 3) 1. Load the data "mtcars" 2. Run the following code. scatterplot3d (wt , disp, mpg , pch=16, highlight . 3d=TRUE, type="h" , main="3DScatterplot") Interpret "pch=16" and "highlight.3d=TRUE" in this code. 3. Plot scatterplot matrices among factors: mpg, cyl and wt. 3 4. Plot barplot with both factors gear and cyl under the title "Cars by gear and cylinder" 5. Plot boxplot of qsec by cyl with title "Speed test".Question 6 (10 marks) Imaging Pty Ltd (Imaging) sells health care and consumer imaging products. Big Bank has a security interest over all of the business and assets of Imaging. Imaging has been struggling financially and has missed a loan repayment due to Big Bank. The loan agreement between Big Bank and Imaging provides that where there is a default in payment Big Bank is entitled to appoint a receiver. On 1 June 2019 Tim is appointed receiver of Imaging. Tim decides to sell the medical imaging assets. He lists the assets on Gumtree and takes the first offer. Tim decides that the medical imaging side of the business is not profitable and dismisses 15 employees. Advise Tim as to his rights and duties as receiver. .The ENDConsider three urns, one colored red, one white, and one blue. The red urn contains 1 red and 4 blue balls; the white urn contains 3 white balls, 2 red balls, and 2 blue balls; the blue urn contains 4 white balls, 3 red balls, and 2 blue balls. At the initial stage, a ball is randomly selected from the urn whose color is the same as that of the ball previously selected and is then returned to that urn. Let X,, be the color of the ball in the ath draw. (a) What is the state space? (b) Construct the transition matrix P for the Markov chain. (c) Is the Markove chain irreducible? Aperiodic? (d) Compute the limiting distribution of the Markov chain. (Use your computer) (e) Find the stationary distribution for the Markov chain. (f) In the long run, what proportion of the selected balls are red? What proportion are white? What proportion are blue
