In a bivariate data, if r(X, Y ) = 0.667, s 2 x = 12 and sy2 = 15, then find the covariance between the variables X and Y and what is the value of r(Y, X)
Department of Statistics Karnatak Arts College, Dharwad B.Com. IV Semester: Business Statistics List of Assignments Maximum Marks:10 Last Date for Submission: On the day of II Internal Test 1. In a bivariate data, if r(X,Y ) = 0.667, σ2x = 12 and σ 2 y = 15, then find the covariance between the variables X and Y and what is the value of r(Y,X). 2. In a bivariate data on x and y, V ar(x) = 49, V ar(y) = 9 and Cov(x, y) = −0.17.5. find the coefficient of correlation between x and y. 3. In a bivariate data, the regression line are 2x− y + 4 = 0 and x− y + 1 = 0. (i). Find x̄ and ȳ. (ii). Find r the correlation coefficient. 4. The following are the marks in Statistics(x) and Mathematics(y) of 10 students in P.U. Examination. Find the coefficient of rank correlation. x 43 96 74 38 35 43 22 56 35 80 y 30 94 84 13 30 18 30 41 48 95 5. The information given below is production of Wheat in certain region of the country in metric tonns. Year 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 Production 68 62 61 65 68 63 67 60 72 70 76 Using three yearly and four yearly moving averages, obtain the trend values. Graph both the original and trend values on the same graph. Years 1964 1965 1966 1967 1968 1969 1970 1971 1972 Sales (in thousands) 67 42 27 04 25 27 76 77 64 6. Explain the differences among the three principal type of indices: price, quantity, and value. 7. The data given below is obtained from the servey to study the price variations and variations in quantity used by the families of important commodities of a certain city : Commodity Base Year Current Year Price (in Rs.) Total Value Total Expenditure Quantity (in kg.) A 120 6000 6600 40 B 100 2000 3300 30 C 140 8400 9800 70 D 160 4800 5600 35 F 180 7200 8000 40 G 220 6600 7360 32 H 200 4000 5250 25 (a) Compute price and quantity indices for the current year using Laspeyre’s, Paasche’s, Marsall- Edgeworth’s and Fisher’s aggregative expenditure methods. (b) Check whether Marsall-Edgeworth’s and Fisher’s Index numbers satisfy time reversal and factor reversal tests by using the above data. 1 8. An enquiry into the budgets of middle class families in a city gave the following information: Group Weights (w) Prices (in Rs.) 2010 2019 Food 30 220 270 Rent 15 260 350 Clothing 20 150 200 Fuel & Light 10 75 100 Miscellaneous 25 160 230 Compute the Consumer Price Index number for the year 2019 using weighted A.M. of price relatives and weighted G.M. of price relatives. 9. Two unbiased dice are thrown. Find is the probability that a sum of the top faces is different from 8 . 10. A bag contains 7 red, 12 white and 4 green balls. What is the chance that 3 balls drawn are all white Instructions to students 1. All the students are hereby informed to submit the clearly, systematically, complete solved assignment On the day of II Internal Test. Information by B.Com. IV semester, Business Statistics, subject teachers 2