Homework questions:-

2 Let C= - Let Y, and Y, be independent random variables with B[ Y ] = 3, E[Y,] = 9, and Var Y, = Var Y, = 16. (a) Find E[ C]. (b) Find E[CY], where Y = (c) Find Var Y. (d) Find Var CY.Let C= Let Y, and Y, be independent random variables with ETY ] = 5, ETY,] = 10, 7 Var Y, = Var Y, = 6. (a) Find E[CY] where Y = (b) Find Var Y. (c) Find Var CY.Consider the simple linear regression model. Are 8, and B, uncorrelated? Explain, based on the variance-covariance matrix.The three basic structural elements of a data processing system are files, flows, and processes. Files are collections of permanent records in the system, flows are data interfaces between the system and the environment, and processes are functionally defined logical manipulations of data. An investigation of the cost of developing software as related to files, flows, and processes was investigated. The following data are based on that study. Cost (in units of 1000) Files Flows Processes ( v) 22.6 44 18 15.0 33 15 78.1 80 80 28.0 24 21 80.5 227 50 24.5 20 18 20.5 41 13 147.6 187 137 4.2 19 15 48.2 50 21 20.5 48 17 Find a 90% confidence interval on Ap.The three basic structural elements of a data processing system are files, flows, and processes. Files are collections of permanent records in the system, flows are data interfaces between the system and the environment, and processes are functionally defined logical manipulations of data. An investigation of the cost of developing software as related to files, flows, and processes was investigated. The following data are based on that study. Cost (in units of 1000) Files Flows Processes (v) (r , ) (x]) 22.6 44 18 15.0 2 33 15 78.1 80 80 28.0 24 21 80.5 227 50 24.5 20 18 20.5 41 13 147.6 187 137 4.2 19 15 48.2 50 21 20.5 48 17 Find a 90% confidence interval on B.\fConsider the following data: 2 3 5 6 17 29 34 46 42 52 For the model of Exercise 38, 2.428571 -1.28571 1428571 (XX]= =-1.28571 .797619 -.0952381 .1428571 -.0952381 .01190476 228 X'y = 1111 6091 3 = 12.27380952 Use this information to estimate the model.Consider the following data: 2 3 5 6 17 29 34 46 42 52 Test an appropriate hypothesis to decide whether the quadratic regression curve significantly fits the data better than the linear regression curve.Consider the following data: 2 3 4 5 6 7 17 29 34 46 42 52 Using the regression curve selected from Exercise 40, compute a 95% confidence interval on Pyx, when x = 4.8.Consider the following data: 2 5 6 17 29 34 46 42 52 Using the regression curve selected from Exercise 40, compute a 95% prediction interval on an individual response when x = 4.8.A research study was conducted on cracking of latex paint on wooden structures. The primary concern in the study is to investigate the effect of water permeability and fracture energy (energy to propagate a crack through paint film) on paint crack rating. The investigation yielded the following data: Sample Crack rating Permeability Fracture energy number (F) (I, ) 2.1 4.31 84 22.11 5.1 11:40 14.5 24.15 44 6.21 6.2 5.65 125 9.71 T.O 12.00 17.2 14.25 7.1 8.63 Plot y versus x, and y versus X2