Assume an economy has a budget surplus of 1,000, private savings of 4,000, and investment of 5,000. Write out a national saving and investment identity for this economy. What will be the balance of trade in this economy? If the budget surplus changes to a budget deficit of 1000, with private saving and investment unchanged, what is the new balance of trade in this economy?

(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".Calculate compound interest Question An account is opened with an initial deposit of $5,500 and earns 2.5% interest compounded annually. What will the account be worth in 10 years? Round your answer to the nearest dollar. Provide your answer below:4. Suppose that n light bulbs are burning simultaneously to determine the lengths of their lives. We shall assume that they burn independently and that the lifetime of each bulb has the exponential distribution with parameter . Let X2- denote the lifetime (in thousand hours) of bulb i, for 2' : 1, . . . ,n. The pdfJ mean and variance of exponential distribution Expw) are 1 1 1%) = fie'93, 1300 = -, Var(X) = 2- 3 X3 (a) What does the central limit theorem say about the distribution of W when n is large? (b) Find a two-sided 95% condence interval of the mean lifetime (1/3). Express your answer in terms of n, X and z (the 2 critical values). Interpret the condence interval you obtain in context of the situation. (c) Now, suppose that we want to test whether or not the mean lifetime is 1000 hours, we would consider H0:,8=1Ha:71. Derive the likelihood ratio statistic. (d) Denote the likelihood ratio statistic by A(X). Should the null hypothesis H0 be rejected when A(X) is large or small? (0) What is the large-sample distribution of 2 log AU?) when the null hypothesis H0 is true? (f) Explain what a Type I error would mean in context of this problem. Q1: (Hypothetical) In IIIE total 800 students applied in MSc programs, 200 in IBF, 250 in Economics and 350 in Economics and Finance program. A test of 100 marks was conducted for admission into these degree programs. Note Following information: marks obtained by Economics students are normally distributed with mean 60 marks and SD 12marks marks obtained by Economics and Finance students are normally distributed with mean 58 marks and SD 13marks Now answer following questions: L How many of the economics students obtained marks between a 35 and 65 b. 20 and 80 C. 5 and 95 ii. Grade "A" is assigned to student who obtained marks 80 or more, how many students of Economics and finance got "A" grade? Suppose in previous MSc IBF class there were 20 students, out of which 5 were foreigners. Suppose 5 students are randomly selected for a group discussion on Islamic and Conventional Banking. What is the probability that a. Exactly three foreigners students are selected b. Less than three foreigners students are selected c. At least three foreigners students are selected d. At most three foreigners students are selected