Business Statistics and Financial Mathematics — DU B. Voc – Banking Operations Previous Year Question Papers

Calculate the Spearman's rank correlation coefficient to determine if there is a correlation between the performance of stocks in Sector A and Sector B. (8) Your Roll N o....,.,..,.,... Financial Mathematics Semester III 3. Each question is of 15 marks J (a) The following data relates to the ages of Iibrary card holders in a particular library scheme. Holders l0-10 20-30 30-.t() i10-50 50-1,0 6()-70 7{)-lit0 Ir0-90 Calculate the quartile deviation. (7) (b) The age distribution of 130 sales executives employed in a business enterprise is given below: Age Number of executives Calculate the distribution. Mode of age from the given 2 (a) A savings account offers an interest rate of 8% compounded monthly. Find the nominal int€rest rate if the effective annual interest rate is 8.3%' $400 at the end of each quarter ior the next 5 years. What is the future value of the annuity3? (b) Consider two sets of data representing the performance of 10 stocks in two different sectors over a period: Sector A Performance Sector B Performance 5 (a) A company fits a simple linear regression model to predict its monthly sales based on advertising expenditure. The observed sales (in thousands of units) for 5 months and the predicted sales from the model are given below: You plan to invest $10,000 in a deferred annuity. The interest rate is 57o per year, compounded annually. You will make annual payments of$1,500 starting in 5 years, and the payments will continue for a total of l0 years. What is the present value of this annuity? (5) Month Observed Sales Predicted Sales (b) A loan officer is studying the relationship between interest rates and the loan amount applicants qualify for. The data from five recent loan applicants is shown below: Calculate the Mean Squared Error (MSE) for the regression model. (8) Applicant Interest Loan Amount (b) Difference Between Parametric and non-parametric tests. (7) (i) Determine the linear regression equatlon to predict the loan amount based on the interest rate. (i) Find the probability that a customer made a purchase, given that they were exposed to the marketing camPaign (ii) Predict the loan amount for an applicant with a 6.250/o interest rate. (10) (ii) Find the probability that a customer was exposed to the campaign, given that they made a purchase. (8) (a) What is Poisson's distribution? Write a formula for probability function of Poisson's distributions' Also find the mean and variance. (7) (a) What is hypothesis? Mention the types of hypotheses testing and steps of the hypothesis procedure? Q) (b) A company launched a marketing campaign to increase product sales. Among the 500 customers, 200 were exposed to the marketing campaign (event E) and 300 were not. Out of the 200 customers who were exposed, 100 made a purchase (event M), and 100 did not. Out of the 300 customers who were not exposed, 50 made a purchase and 250 did not. (b) A manufacturer claims that the average lifetime of a lightbulb is 800 hours. A sample of 25